Closed-loop stability conditions are given for systems with both structured and unstructured uncertainties. In particular, it is shown that the guaranteed cost regulator taking into account the structured uncertainties, can tolerate unstructured uncertainties as well, If the systems dynamics matrix only is uncertain, this controller provides the same stability margins as the standard LQ optimal regulator, for all admissible parameter variations. If, in addition, uncertainties enter into the input matrix, stability margins depend on the uncertainties on B. Furthermore, these results are extended to the a-stability case.