This work presents results on the stability of time-delay systems under reset control. The case of delay-dependent stability is addressed by developing a generalization of previous stability results of reset systems without delays, and also the case of delay-independent stability. Stability conditions are given by using a set of LMIs and passivity properties. These conditions guarantee that the reset action does not destabilize the base LTI system. Finally, limitations and future directions are discussed by describing function analysis.