The dynamics of a two-phase multicomponent reservoir system which is approaching the steady-state flow regime are studied. First, the compositional model is analyzed in the linear approximation, for the case of a small initial deviation from the steady-state regime. An analytical expression is obtained for the characteristic relaxation time. Next, numerical simulations are performed for situations where there is a substantial deviation from the steady-state regime. The linear injection of an enriched gas into a gas-condensate reservoir, followed by the extraction regime, is simulated. It is shown that the change in phase compositions and pressure on the way to equilibrium proceeds with characteristic times of the order of the injection time. However, the change in the saturation and overall composition takes approximately 200 times longer than the injection time. Thus. the reservoir system manifests a spatially inhomogeneous saturation distribution for an abnormally long time. Similar kinetically stable patterns have been also discovered in the nonlinear dynamics of phase transitions, plasma, and thin films. The question of the existence of discontinuous steady states for this multicomponent flow is considered. In the case of a binary mixture, it is shown that such solutions do not exist(1).