A numerical model was used to examine the consequences of transience and nonlinearity in the critical-level interaction of an internal gravity wave. Wave packets in a shear flow were observed to evolve as predicted by the linear, initial-value results of Booker and Bretherton (1967) until convectively unstable layers evolved. Once formed, such layers were found to break down via a convective instability, presumably resulting in the turbulent dissipation of the incident wave packet. Several simulations were used to illustrate the transient stabilization of, and the Eulerian mean flow accelerations induced by, critical-level interactions. Other simulations were performed to examine the evolution of a wave packet in a time-dependent shear flow. The latter suggest that critical-level absorption and wave action dissipation can be either greatly accelerated or effectively eliminated depending upon the tendency of the main velocity shear. The implications of these findings for internal gravity wave propagation in the atmosphere and the oceans are discussed.