This paper provides complete results on the stability behavior of a class of uncertain dynamical systems with jumping parameters and functional time-delays. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. The parametric uncertainties are norm-bounded appearing in all system matrices and the delay factor depends on the mode of operation. Notions of weak and strong stochastic stability for the jumping system are developed depending on the available information using a prescribed H-infinity-performance. Memoryless and delayed-state feedback are considered to guarantee the closed-loop stability. All the results are cast into linear matrix inequalities format. A numerical example is given to illustrate the developed results. (C) 2003 Elsevier Ltd. All rights reserved.