We provide a convergence theory for adaptive learning algorithms useful for the study of learning by economic agents. Our results extend the framework of Ljung (1977) previously utilized by Marcet-Sargent (1989a, b) and Woodford (1990), by permitting nonlinear laws of motion driven by stochastic processes that may exhibit moderate dependence, such as mixing and mixingale processes. We draw on previous work by Kushner and Clark (1978) to provide readily verifiable and/or interpretable conditions ensuring algorithm convergence, chosen for their suitability in the context of adaptive learning.