In this note is studied the delay-independent stability of delay systems. It is shown that the strong delay-independent stability is tantamount to the feasibility of certain linear matrix inequality, or equivalently to the existence of certain quadratic Lyapunov-Krasovskii functional, independent of the (nonnegative) value of the delay. This constitutes the analogue of some well-known properties of finite-dimensional systems. This result is then applied to study delay-independent stability of systems with commensurate delays, delay-independent stabilizability, and delay-indepen- dent stability of systems with polytopic uncertainties.