Four-wave-mixing nonlinear-response functions are given for intermolecular and intramolecular vibrations of a perpendicular dimer and intramolecular vibrations of a square-symmetric molecule containing a doubly degenerate state. A two-dimensional particle-in-a-box model is used to approximate the electronic wave functions and obtain harmonic potentials for nuclear motion. Vibronic interactions due to symmetry-lowering distortions along Jahn-Teller active normal modes are discussed. Electronic dephasing due to nuclear motion along both symmetric and asymmetric normal modes is included in these response functions, but population transfer between states is not. As an illustration, these response functions are used to predict the pump-probe polarization anisotropy in the limit of impulsive excitation.