A two-dimensional vibrational system with a strong nonlinear coupling is studied using a quantum-classical mixed mode self-consistent-field approach. The classical equations of motion as well as the time-dependent Schrodinger equation are solved for respective modes under the influence of the average fields generated by the other modes. This vibrational system was previously shown to be chaotic under classical mechanical treatment but quantum mechanical observations pointed out to highly regular behaviour. The results of the mixed mode calculations give periodic trajectories, regular Poincare maps and Lyapunov numbers, k = 0. These observations support the previous findings that during the transition from classical to quantum mechanics, regularity dominates the dynamical behaviour.