Results following from time reversal symmetry are developed for those nonlinear optical processes where a statistical average is required. This extends results found in Rayleigh (and Raman) scattering to nonlinear optical processes of arbitrary order, and generalises those few analyses specific to nonlinear optics. For example, Onsager relations for self-conjugate nonlinear optical processes (when input and output photons form degenerate pairs) are derived, and associated reversality relations generalised. In the nonresonant limit magnetic dipole but not electric quadrupole terms in coherent processes are suppressed. For this and other selection rules a careful treatment is required to obtain gauge invariant conclusions since the relevant electronic operators in multipolar and Coulomb gauges have differing time reversal signatures. For general processes purely electric dipole contributions to natural optical activity are possible when intermediate resonances are present; strong resonances are not required for the domination of this contribution over the traditional contribution. Time reversal symmetry may be used to show the prescription for assigning signs to phenomenological damping factors that is usually associated with the optical susceptibility formalism is incorrect. An experimental test based on electrooptic rotation in fluid media is proposed which may distinguish between this incorrect prescription and the correct prescription. The role time reversal symmetry plays in restricting the number of parameters in Judd-Ofelt theory is elucidated.