Ahmedeltigani Alsyed, 19, of Hounslow, and a 17-year-old from Merton, are each charged with a count of preparation of terrorist acts and collection of information contrary to section 58 of the Terrorism Act 2000.
The four appeared together in the dock and were ordered to appear at the Old Bailey on March 17.
The 15-year-old, of Waltham Forest, appeared in a separate youth hearing at the same court.
He pleaded not guilty to one charge of possession and two counts of dissemination of terrorist publications and is due to stand trial on May 2 at Westminster Magistrates' Court.
Four of the teenagers were arrested at addresses in south and west London on Tuesday while the 15-year-old boy was arrested on Monday evening in east London.