In this paper we analyse the stability robustness of linear continuous-time and discrete-time systems with structured time-varying uncertainties. The system to be controlled is described by the usual state-space formulation but includes time-varying uncertainties. The first new robust stability sufficient condition we have derived in this paper may become the necessary and sufficient condition of system stability in some situations. The second new condition is always less conservative than the sufficient condition recently proposed by Sobel et al., (1989). The third new condition, using the similarity transformation, provides the possibility of getting even less conservative results. In deriving these new conditions we also present some new lemmas which are valuable in related research. The results are extended to linear discrete-time systems and some illustrative examples are given.