The problem of optimal model-following linear control of discrete stochastic adaptive systems is studied in the presence of unmodelled dynamics. The controller complexity is restricted to that corresponding to the perfectly modelled situation. The key for a control design to be robust in the presence of unmodelled dynamics is closely related to some parametrical conditions that ensure a certain linear filter (involving parametrical uncertainties related to unmodelled dynamics) maintains the output stationarity of any stationary random input signal, as in the nominal situation. Partial results concerning robustness are obtained from stability considerations. In any case,a prioriknowledge on the unmodelled dynamics is not available for the implementation of the control law.