Last year Parker said more than 500 people had contacted them about potential claims.
The first Harditex claim was brought by Tracey Cridge and Mark Unwin, who claim their Wellington home suffered widespread internal water damage - estimated to cost more than $300,000 to fix.
Another Wellington couple, Katrina Fowler and Scott Woodhead, have also claimed over their 2000 duplex.
James Hardie denies the claims and has said it stands by the integrity and quality of its building products.
It would vigorously defend any allegations made against its products, it said when the class action was revealed last year.
The company was founded in Melbourne in 1888 by Scottish immigrant James Hardie. It is now listed on the Australian and New York stock exchanges and has its headquarters in Dublin.
In the 2016 financial year it generated net sales of $US1.73 billion ($NZ2.44b).
- AAP