In this note we find an explicit expression for the eigenvalues of a retarded time-delay system with one delay, for the special case that the system matrices are simultaneously triangularizable, which includes the case where they commute. Using matrix function definitions we define a matrix version of the Lambert W function, from which we form the expression. We prove by counter-example that some expressions in other publications on Lambert W for time-delay systems do not always hold. (c) 2007 Elsevier Ltd. All rights reserved.