In this paper, the robust adaptive control design problem is studied for a class of non-triangular nonlinear systems with unmodeled dynamics and stochastic disturbances. It is assumed that the states of the systems to be controlled are unmeasurable, and thus an adaptive state observer is first developed. By utilizing the stochastic small-gain theorem and the backstepping recursive design procedure, a robust adaptive output feedback control scheme is then proposed. It is shown that all the signals in the resulting closed-loop system are bounded in probability, and the system output converges to a small residual set of the equilibrium in probability. (C) 2017 Elsevier Ltd. All rights reserved.