In Physica A 237 (1997) 113, we have proposed in terms of Gaussian white noise (GWN) a generalized method, in terms of eigenfunctions and eigenvalues, of the quasideterministic (QD) approach and its connection with the nonlinear relaxation times (NLRT) to describe the transient stochastic dynamics of multivariate systems. Contrary to what happens with the standard formulation of QD approach, the generalized theory is focused on those unstable systems, which are not necessarily derived from a potential function. In the present work, we extend the generalized method to the case of Gaussian colored noise (GCN). The coupling between the noise and the initial state of the system, as a natural effect in colored noise problem, is also addressed. To justify the theory, we study the same two analytical models, in two and three variables, of the preceding reference and calculate the time scales associated with those models.