Vibronic coupling of the Herzberg-Teller type is discussed as a possible source of the depolarization dispersion of a fundamental line of a totally symmetric vibration in resonance Raman scattering (RRS). Two cases are discussed separately. The first case concerns RRS from an electronic state that borrowspart of its intensity from a non-overlapping electronicstate of different symmetry. In this case the depolarization ratio of the fundamental line for right angle scattering linearly polarized light can vary between the limits Q and $. The second case arises when part of the intensity is borrowed from an electronic state of the same symmetry but with a transition moment non-parallel to that of the resonant state. Such a situation can occur in molecules with a symmetry corresponding to one of the following point groups: C . In this situation the depolarization ratio pi can vary between the limits; and Q). In both cases the amplitude of the variations of p, depends on the damping constant. In the second case the value of the displacement parameter of a totally symmetric mode has a major influence on the range of change of p,. Both cases show prominent resonance-antiresonance coincidences between depolarization dispersions and excitation profiles, which has been previously predicted for non-totally symmetric modes, and for molecular dimers. It is pointed out that the depolarization ratio in the preresonance region is very sensitive to vibronic coupling and can serve as a probe of such coupling.