Previously, a treatment of the vibrational contribution to nonlinear optical properties for molecules with large amplitude modes in a symmetric double-minimum potential well was devised. The vibronic energies were written as a power series in the field for two limiting cases of the ratio between the field-induced energy and the zero-field splitting energy of the two lowest vibronic states. This treatment is extended here to include all values of the ratio and also an asymmetric double-well potential. It is shown that a consistent treatment of NLO effects in the general case leads to new field expansion coefficients, which are formulated in terms of the usual dipole moment and (hyper)polarizabilities. As an example, the new treatment is applied to the inversion motion of CH3- ; We thank David Lauvergnat for helpful advice concerning the programs TNUM and ELVIBROT. H.R, J.M.L., and. MG.-B. gratefully acknowledge support from the European Union (MTKD-CT-2006-042488). J.M.L. and M.G.-B. thank the Spanish Ministerio de Ciencia e Innovacion (MICINN, CTQ2011-23156/BQU) and the DIUE of the Generalitat de Catalunya (2009SGR637) for financial support. M.G.-B. thanks the Spanish MEC for a doctoral fellowship (No. AP2010-2517)