Correlated-basis-function perturbation theory is used to evaluate the zero-temperature response S(q,ω) of 3 − 4 He mixtures for inelastic neutron scattering, at momentum transfers q ranging from 1.1 to 1.8 A ˚ − 1 . We adopt a Jastrow correlated ground state and a basis of correlated particle-hole and phonon states. We insert correlated one-particle–one-hole and one- and two-phonon states to compute the second-order response. The decay of the one-phonon states into two-phonon states is accounted for in the boson-boson approximation. The full response is split into three partial components S α β (q,ω), each of them showing a particle-hole bump and a one phonon, δ-shaped peak, which stays separated from the multiphonon background. The cross term S 34 (q,ω) results to be of comparable importance to S 33 (q,ω) in the particle-hole sector and to S 44 (q,ω) in the phonon one. Once the response has been convoluted with the experimental broadening, the computed scattering function is in semiquantitative agreement with recent experimental measurements.