In this payer, we address the analysis and state-feedback synthesis problems for linear parameter-varying (LPV) systems with parameter-varying time delays. It is assumed that the state-space data and the lime delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. We explore the stability and the induced L-2 norm performance of these systems using parameter-dependent Lyapunov functionals. In addition, the design of parameter-dependent state-feedback controllers that guarantee desired L-2 gain performance is examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved via efficient interior-point algorithms.