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The problem of data compression for communication networks is considered. The system performance criterion is the signal distortion resulting both from data compression and from average message delay through the network. The delay-distortion function is defined as the smallest message delay among all data-compression schemes that yield the given distortion value. The distortion-delay region is similarly defined. The capacity region is defined to include all incoming message rates for which there exists a set of data-compression schemes yielding a prescribed network distortion-delay value. The basic characteristics of these functions and regions are derived. In particular, it is shown that their evaluations can be performed by solving separately the source coding problem and the network's queuing problem. The distortion-delay functions and regions are explicitly derived for single channel systems.