THIS PAPER BELONGS to that part of economic dynamics of which the consumption turnpike theorems are typical results. However, rather than the usual formulation of the problem as a mathematical programming problem, we study it in the framework of dynamic equilibrium models which were first studied in [9]. In [9] we considered finite equilibrium trajectories for which the technology as well as demand functions were assumed constant in time. Here a more general model will be described. It permits changing technology and demand functions and pays more attention to the exploration of the asymptotic properties of infinite trajectories. We define the class of efficient equilibrium trajectories and prove that, under certain conditions, infinite trajectories in this class converge to each other. Finite trajectories (which are always efficient) may differ essentially from them only at the beginning and at the end of the planning period. For a stationary model a strong turnpike theorem follows from these considerations. It is shown that nonefficient equilibrium trajectories are characterized by fast growth of prices and high levels of production. At the same time, the consumption, as a rule, goes to zero. Here we present conditions which imply the uniqueness of efficient trajectories and the absence of nonefficient ones. For the special case in which the equilibrium model is equivalent to an optimization model, efficient equilibrium trajectories are strongly optimal.