The low-energy excitations of filled Landau levels (LL's) of electrons involve promotion of a single electron from the topmost filled LL to the lowest empty LL. These are called excitons or collective modes. The incompressible fractional quantum Hall states are understood as filled LL's of composite fermions, and the low-energy neutral excitations are excitons of composite fermions. New techniques are developed to study large systems, which provide detailed information about the dispersions of the composite fermion excitons. In particular, it is found that the interaction energy of the exciton is well described by the `unprojected' composite fermion theory.

40 pages including 13 postscript figures; accepted for publication in Physical Review B (1996); related paper in cond-mat/9511136