Abstract: A system for transmitting data between distant locations comprises a modem at each location and a communication channel, typically a telephone line, whose transfer function has a principal component whose variation is slow and a second component whose variation is faster, but whose action is lesser. A correction device is located in the modem at the output of the channel and comprises an equalization filter constructed to compensate for the principal component and a digital adaptive network having a few coefficients and a low time constant, compatible with the frequency of the second component. The coefficients of the digital network may be adapted independently of those of the equalization filter.