In this paper a class of integrated voice/data multiplexers with an automatic repeat request (ARQ) scheme is analysed using a two-dimensional Markov renewal process model. The ARQ schemes considered are stop-and-wait and go-back-N methods. To obtain mean data message de/ay we use an approximation in which we assume that the data service capacity does not change during the service time of a data message. The results are validated by simulation. Also, to verify the approximation method we consider a technique of parameter change by which we obtain the mean data message delay exactly in a voice/data multiplexer with a variable service capacity. Unfortunately, however, the exact analysis method does not always work because of its computational complexity especially when the system is large.