You don't hear much about "the family business" nowadays, except, it seems, in one particular occupation.

Search for pop stars' offspring involved in "proper jobs" - those unconnected with the entertainment business - and you'll be hard pushed to scrape together more than a few examples.

Because, faced with an uncertain future, most offspring of the musical classes soon decide that they'd like a bit of what mum and dad have got, thanks very much. And since mum and dad still have a bit of pull in the industry, they're more likely to get a crack at it.

The results frequently merely litter the record racks and gossip columns, but in quite a lot of cases, the family business does appear to work.

Jason Bonham and Zac Starkey are not bad drummers, Dweezil Zappa can run rings around most lead guitarists, and both Jeff Buckley and Rufus Wainwright proved to have decent pipes. And the closer one gets to the points where folk and country rub up against rock and pop, the more crowded things get, with the likes of Eliza Carthy, Martha Wainwright and Carlene Carter merely the tip of an iceberg of burgeoning dynastic talent.

"There's a whole generation of them," noted Rufus and Martha's dad Loudon Wainwright III when I asked him about the folkie kids a few years ago. "Richard Thompson's son, Pete Townshend's daughter, Leonard Cohen's son - they should all form a football team."

Two such musical offspring recently released albums in which the family connection is integral. Return of the Son Of... is the latest album by Dweezil Zappa, whose Zappa Plays Zappa ensemble is a group dedicated to performing his late father Frank Zappa's music as faithfully as possible.

The Gift is Eliza Carthy's first release as a duo with her mother Norma Waterson, partly comprising songs that have a personal resonance to their relationship; the notion of family tradition is further cemented by their dedication of the album to their late friend, folk singer Kate McGarrigle, mother of Rufus and Martha Wainwright, and matriarch of the North American equivalent of the Carthys' first-family-of-folk status.

Martin Carthy claims one of his and wife Norma Waterson's finest achievements is to have produced a daughter as talented as Eliza. "She's adventurous in the extreme, a great example," he says, proudly. Eliza, of course, was brought up surrounded by singing. "There's early memories of being asleep under stages at festivals, while they do their gig," she recalls. "Or listening to them having big singing parties downstairs - they'd put me to bed, but I'd know they were having fun down there, so I'd sneak down and sit under the kitchen table listening to them play their instruments.

"They always had really interesting guests, like this very nice American banjo, fiddle and guitar player called Jody Stecher, who was touring with this Indian sitar player Krishna Bhatt - watching the cross-over between old-time-y music and Indian classical music was really interesting."

Carlene Carter, daughter of June Carter and step-daughter of Johnny Cash, also remembers mom and pop's musical chums dropping by - except that, with Johnny Cash, these were sometimes showbiz legends.

"We'd have this thing where you'd sing for your supper," she explains. "You'd pass the guitar and play a song, or tell a story, tell a joke. It was really fun, because all these incredible people would be there. One time, Paul McCartney sat down at my tick-tack piano and played 'Lady Madonna', and I went, 'holy shit!' How do I follow that?"

For most showbiz kids, the family business is something they absorb naturally, soaking up musicality as a way of life, all the more so when it's rooted in the intimacy of harmony singing, as in Carlene's case with The Carter Family.

"There's something about singing with family that's really cool," she enthuses. "It's like osmosis: you immediately know where you're going. My aunt could tell if I was a little bit off - she'd give me this look, and if she nodded up I'd go up a little, and if she nodded down, I'd go down a little. All summer long, they'd be playing these dinky little fairs with amusement parks, and me and my sister would be riding rides all day long, while they'd be playing three shows a day. We'd go up and sing at the end, then we'd run off and ride the roller-coaster again."

Her mother taught Carlene to play boogie-woogie piano when Carlene was five years old, and from that moment she was hooked. Her first guitar lessons came from her grandma, "Mother" Maybelle Carter, who taught Chet Atkins how to play. But when Johnny Cash bought ten-year-old Carlene her first electric guitar, it was the imported blues-rock of Cream, Hendrix and The Yardbirds to which she was drawn.

"Actually, I didn't listen to much country music at all when I was growing up," Carlene Carter admits. "The only country music I knew was Carter Family music, period. My mom brought home Bob Dylan's first record when I was, like, six years old, and she sits me down in the living room and says, 'this young man is going to change music forever'. That's how musical my mom was. She taught me to be open to all types of music. She really wanted me to go to Juilliard and study classical music!"

One second-generation musician who probably got as good a grounding in classical music at home as he would have found in any conservatoire was Dweezil Zappa, son of guitarist Frank, and now a considerable guitarist and bandleader in his own right. Up until around the age of 12, Dweezil and his siblings heard little but their father's music, since they never listened to the radio.

"Growing up I didn't hear anything other than what he was working on, or listening to recreationally, which could be anything from a Shostakovich piano concerto to the Bulgarian Women's Choir, to rhythm and blues," recalls Dweezil. "I got exposed to a lot of things I wouldn't otherwise have known about, everything from Webern to Stockhausen. He'd ask me, 'do you like this?', and it might be some atonal thing that did not have a strong emotional connection to me as a 12-year-old, and I'd say, 'I don't like this one quite as much as some of the other ones', and he'd say, 'me too!"'

Frank also encouraged the hands-on involvement of his kids in music, for his own ends, to enable him to hear complex dissonant chords. "He would sit in the living room playing the piano," his widow Gail recalled, "until enough of the kids came through the room and he could say, 'hey, could you put your hands on that part of the keyboard', and then he could play the chord he wanted to hear."

Unsurprisingly, this kind of early exposure to avant-garde techniques and sounds left a deep impression on the young Dweezil when he finally reached his teenage years and started hearing things like The Beatles and Led Zeppelin and Van Halen.

"I knew my dad's music was different," he says. "It was far more orchestral and complex, so when I started hearing other music I thought, 'I like this, but I'm missing some of these other elements that I'm so used to, all these other details'. Sometimes, regular music is not enough!"

And while Eddie Van Halen was the young Dweezil's first guitar hero, it was quite natural that he should pick up something of his father's distinctive guitar style when he took up the instrument himself. These days, he runs Zappa Plays Zappa, an ensemble dedicated to performing dazzling versions of knuckle-knotting items from the Frank Zappa repertoire.

Unlike Dweezil, her own father's instrument was not Eliza Carthy's first choice. "I never got my head around the guitar," she admits. "My dad was away so much when I was a kid, so there were never any guitars around the house! My mum got me formal piano lessons when I was eight, but I gave it up when I went on the road - it's the old joke about not being able to get a piano on your back! I had violin lessons too, but it wasn't until I was about 15, when I met the Northumberland violinist Nancy Kerr, that I suddenly got interested in it. Within 18 months, I was away on the road, a professional fiddle player. Nancy was a real role model for me when I was growing up."

Positive role models are not easy to come by in the music business, certainly as far as the non-musical aspects of the musical life are concerned. Carlene Carter, for instance, remembers Johnny Cash's amphetamine addiction almost torpedoing his relationship with June Carter.

"Mama wouldn't let him be around us at the time," she recalls. "She wouldn't marry him until he was clean, she wouldn't let him in the house if he was high. He tried really hard to keep between the lines, because he loved mama. But everybody is not perfect, it doesn't work that way, and we all trip and fall."

Carlene herself would fall into drug addiction years later, before emerging sadder and wiser, though no less ebullient, with her excellent comeback album Stronger a couple of years ago. There is, however, a certain irony in the way that the supposedly conservative, god-fearing world of country music has habitually been riddled with boozers and druggies, from Hank Williams, George Jones and Johnny Cash on down, while the man who at one time presented the freakiest public face of opposition to conservative, establishment values, Frank Zappa, banned drugs from his band The Mothers of Invention, and frequently lambasted both booze and drug cultures in his satirical cantatas.

All the same, it must have been difficult, I suggest to Dweezil, for him to do the whole teen-rebellion thing with a father as weird as Frank.

"For me to rebel in my family, I would have needed to become an accountant or a lawyer!" he admits. "But I always had so much respect for my parents I never got involved in all the crazy stuff - I've never taken a drug in my life, never smoked a cigarette, never got drunk. Which for a Hollywood family is rare - all these other kids have been to rehab hundreds of times. I've had people offer me a drink, and when I say, 'no thanks, I don't drink', they say, 'how long have you been sober?'! Only 40 years!" But for most musicians' families, it's the separation that does the most damage, with the more successful and in-demand artists being away on tour the most.

"I remember my parents being away for long periods of time, going off on tour for two months," recalls Eliza Carthy. "One time in the Eighties, my mum came back from touring America and she'd cut her hair - she used to have this long black hair all the way down to her arse, and she came back with this perm. I remember rushing out to greet her, and not recognising her, just screaming and running back in! It must have been awful for her, because now I know exactly how she must have felt - my daughter's 18 months old and she really feels it when I go away."

Which brings up the possibility of yet another generation of musical offspring coming along in a few years' time, a dynastic prospect that some regard with relish. Dweezil Zappa's children, aged two and four, can already recognise grandad's theme tune Peaches en Regalia, and Dweezil enthuses like most parents about their early musical efforts, specifically his eldest daughter's first song.

"I laughed so hard!" he says. "She was playing these really atonal cluster chords at this little piano and singing this little melody, with the words, 'sheeps and garlic'. She gets really into it when I ask her to play it, it's become a real performance. It's like a hit song to me now!"

Eliza Carthy is similarly entranced by her own daughter Florence's musical efforts. "We make up songs about poo, and mud, and cats and things," she says. "Florence loves that! When she sees a bee around the house, she goes, 'bee, bee bee, bee' - she doesn't have a great deal of words, but she seems to have a good pair of lungs on her!" Florence's grandad Martin, too, is convinced that she'll follow in the family business.

"One of the reasons Eliza's a musician," he believes, "is that Norma was doing gigs right up to two weeks before she was born, and Eliza heard all that racket. And Eliza was singing up to three weeks before Florence was born, so she heard that racket too.

"It's what folk music really means: it's family music, it goes through the generations, and relies on people passing it on."

-The Independent