This paper presents an effective numerical algorithm for testing the BIBO stability of fractional delay systems described by fractional-order delay-differential equations. It is based on using Cauchy's integral theorem and solving an initial-value problem. The algorithm has a reliable result which is illustrated by several examples, and hence is practically useful in the analysis and design of feedback control for both integer- and fractional-order systems having time delays. (c) 2006 Elsevier Ltd. All rights reserved.