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We present a time-dependent multizone code for simulating the variability of synchrotron self-Compton (SSC) sources. The code adopts a multizone pipe geometry for the emission region, appropriate for simulating emission from a standing or propagating shock in a collimated jet. Variations in the injection of relativistic electrons in the inlet propagate along the length of the pipe, cooling radiatively. Our code for the first time takes into account the nonlocal, time-retarded nature of SSC losses that are thought to be dominant in TeV blazars. The observed synchrotron and SSC emission is followed self-consistently, taking into account light-travel time delays. At any given time, the emitting portion of the pipe depends on the frequency and the nature of the variation followed. Our simulation employs only one additional physical parameter relative to one-zone models, that of the pipe length, and is computationally very …