Abstract We study the asymptotic stability of infinite horizon concave programming problems. By generalizing our preceding work we provide a one-parameter family of conditions that guarantee convergence of the optimal paths to a stationary state. We call this property θ-acyclicity. In the one-dimensional case we show that super-modularity implies our property but not vice versa. We apply θ-acyclicity to a pair of models which study the dynamic behaviour of firms that have adjustment costs. The first is the familiar model of competitive equilibrium of an industry in the presence of adjustment costs. In the second firms act strategically and we study the dynamic evolution implied by the closed-loop Nash equilibria. Journal of Economic Literature Classification Numbers: C61, C62, C73, D92.