An adaptive predictive control algorithm is presented for nonlinear moving average systems with parametric uncertainty. The algorithm is developed in the stochastic optimal control framework in which the parameters are modeled as random processes and their probability distributions are recursively updated and used explicitly in the optimal control computation, The framework yields an open-loop optimal feedback control (OLOFC) algorithm in which open-loop optimal input trajectories minimizing the expectation of a multistep quadratic loss function are computed repeatedly as feedback updates occur. The algorithm is shown to be robust with respect to parametric uncertainty, with features such as on-line parameter refinement (and/or adaptation) and "cautious control". Some potential additions to incorporate an active-learning feature to an otherwise passive-learning OLOFC are considered. Numerical examples are provided to illustrate the merits of the proposed method.