On Critical Delays for Linear Neutral Delay Systems In this work we address the problem of finding the critical delays of a linear neutral delay system, i.e. the delays such that the system has a purely imaginary eigenvalue. Even though neutral delay systems exhibit some discontinuity properties with respect to changes in the delays, an essential part in a non-conservative stability analysis with respect to changes in the delays, is the computation of the critical delays. We generalize, under some minor assumptions on the delay system, previous results on critical delays and stability switches for retarded time-delay systems. The work starts with stating a general equivalence theorem with the spectrum and the matrix function condition. We show how this theorem can be applied to the commensurate time-delay system to compute the critical delays. It turns out that the resulting method is a closely related to parts of the results of Fu, Niculescu and Chen\cite{Fu:2006:NEUTRAL}. For the incommensurate case we present a scheme which allows the computation of the critical curves, i.e. the points in delay-space for which the system has a purely imaginary. We apply the method to previously investigated examples, and hence provide a verification of the results, as well as some examples for which the stability picture is not believed to be known.