Robustness of the stochastic adaptive systems with unmodelled dynamics and external disturbances is discussed in this paper. An adaptive controller is designed using the ELS algorithm except for the finite switches. It is shown that the closed-loop system is globally stable; both the estimation error and the tracking error approach their minima when the unmodelled dynamics diminish, that is the asymptotically adaptive system operating with the ELS algorithm has a good robustness with respect to unmodelled dynamics and external disturbances.