In molecular systems where only a small set of active vibrational coordinates couples to electronic transitions a description by means of a reduced density operator becomes possible. For such systems it will be demonstrated that in the case of a nonlinear coupling between active and passive vibrational coordinates: (i) the passive-coordinate correlation function incorporates a time-independent part, and (ii) resulting from this, the standard Redfield theory which is of the Markovian type cannot be further applied. The respective non-Markovian dissipative dynamics are discussed for a simple model system, and in particular, the reasonableness of a time-independent correlation function is demonstrated. For cases where the constant part of the correlation function dominates, the related non-Markovian density matrix equation can be solved analytically and its solution is shown to be formed by two non-interfering wavepackets.