This note is concerned with stability properties of linear time-invariant delay systems. We consider delay systems of both retarded and neutral types expressed in state-space forms. Our main goal is to provide a computation-oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability. Our results show that this can be accomplished by computing the generalized eigenvalues of certain frequency-dependent matrices. Based on these results, we also state a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems. Our results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units.