The dynamics of vibrational energy relaxation by collisions in molecular beams and free jet expansions are examined. Within the stochastic approach afforded by the use of the master equation, the incomplete relaxation process may be modelled by assuming a time-dependent transition rate matrix. In particular, we prove that for non-degenerate levels and weak interactions the state distribution is Boltzmannian if the transition rate matrix is of the Landau-Teller type. The ramifications of this result on the analysis of recent studies of vibrational relaxation in seeded beams is briefly discussed.