Doubly differential cross sections for ejection of secondary electrons by fast ions have been calculated using linear combinations of products of atomic orbitals with 'inter nuclear' wavefunctions which asymptotically represent incoming and outgoing states. Numerical results for incident protons on He and H2 targets are compared with experiments. The behaviour of the cross sections in the forward peak of the experimental angular distribution, previously unaccounted for in the Born and binary-encounter calculations, is reproduced quantitatively.