The three-dimensional (3D) vibrational spectroscopies are theoretically considered in terms of the associated nonlinear response functions. Since the 3D vibrational spectroscopy involves three vibrational coherence evolutions in the ground electronic state, it is found that there are eight distinctive possibilities when a vibrational coherence state can be created via an infrared field-matter interaction or two off-resonant optical field-matter interactions via Raman. The nonlinear response functions associated with eight distinctive 3D vibrational spectroscopies, where seven of them are novel methods, are presented and expressed in terms of the linear response functions by taking the lowest-order contributions. The analytic expressions of the 3D Fourier spectra are obtained. By using the results, how to utilize the 3D vibrational spectroscopic methods to measure the higher-order vibrational mode coupling arising from the anharmonicity of the multidimensional potential energy surface as well as from the nonlinearity of the dipole moment or polarizability with respect to the vibrational degrees of freedom is discussed. Numerical calculations of the results for a three-oscillator model system are presented, and a few characteristic peaks uniquely appearing in the 3D vibrational spectra are discussed in detail. Finally, the third-order nonlinear terms of dipole moment and polarizability are found to be of critical use in the structure determination, assuming that the collective dipole moment and polarizability is mainly determined by the dipole-induced-dipole interaction effect. (C) 2000 American Institute of Physics. [S0021-9606(00)01209-5].