In this note we study stability properties of linear time-invariant delay systems given in state-space form. We consider specifically the notion of asymptotic stability independent of delay. Systems with both commensurate and noncommensurate delays are investigated. We present for each class of systems a necessary and sufficient conditions in terms of structured singular values, and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems. Our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work.