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In this paper, tandem links with burst errors are analyzed using the Gilbert model for individual links. The results, apart from being of general interest, are of particular relevance to the Integrated Services Digital Networks (ISDN) for which the International Telegraph and Telephone Consultative Committee (CCITT) is currently developing performance specifications based on hypothetical reference connections (HRX's), i.e., composite channels consisting of several tandem reference circuits. The average error rate, the error gap distribution, its mean, and a tight upper bound on its standard deviation are analytically derived for the composite channel (equivalent to an HRX) with tandem links (circuits). These statistics are then related to the performance measures proposed for ISDN. Some numerical results are presented to highlight the large differences in the estimated performance with a burst-error model approach and with an independent-error approach (having identical average error probabilities).