The hyperpolarizabilities for electric dipole second-harmonic generation (SHG) due to the bilinear combination of an electric field and either the electric-field gradient (mu(eeq)) Or the associated magnetic field (tau(eem)), and for electric quadrupole SHG quadratic in the electric field (mu(qee)) have been calculated for the C-60 molecule at pump photon energies from 0.5 to 2.2 eV using the valence effective Hamiltonian method with a minimal STO-3G basis; magnetic dipole SHG quadratic in the electric field (tau(mee)) is zero by symmetry in C-60 The coefficients exhibit resonances at photon energies near 1.9 for mu(eeq), 1.4 for mu(qee), and 2.0 eV for tau(eem). They are combined with empirical local-field factors and a theoretical local field-gradient tenser to calculate the composite susceptibility chi((2)) for SHG from crystalline C-60 in the same energy range. The susceptibility shows several resonances that arise from those in mu(eeq), mu(qee) and tau(eem). The results are able to reproduce the magnitudes and signs reported experimentally, subject to a sensitive dependence on photon energy near resonances.