A modem which may operate as a transmitter or receiver, is provided for use on a line carrying an A.C. signal. The modem comprises a pseudorandom code generator which produces a pseudorandom code signal of a frequency an integral multiple of the A.C. signal frequency. Synchronization means synchronizes the code signal with the A.C. signal. Preferably a coherent system is provided in which a data signal involved has a bit rate an integral multiple of the A.C. signal frequency and in which a carrier generator is additionally provided to produce a carrier signal of a frequency an integral multiple of the A.C. signal frequency. In such case, the synchronization means also synchronizes the data bit and carrier signals with the A.C. signal.