A system for the contactless exchange of data between a transceiver and a passive data carrier is described. A prior data carrier comprises at least one digital memory and at least one digital control device for the memory. In it, the data carrier has a single-coil receiver circuit connected to a controllable switch device. In operation, the data carrier provides, in response to an electromagnetic a.c. field generated by a transceiver, via at least one rectifier, supply power for active components of the data carrier and clock signals for the control of digital components of the data carrier. According to the present invention, in order to provide for the possibility of bi-directional data exchange between a transceiver and a passsive data carrier, and in general, to provide a universally applicable data exchange system of the contactless kind, the transceiver is equipped with a modulator for amplitude modulating the a.c. field. The control device has two inputs for the supply of clock signals and data signals and includes level detectors cooperating with the inputs and arranged to allow the passage of an input signal voltage exceeding a pre-determined value as a valid input signal pulse. The coil is connected to the inputs through a two-branch voltage divider so that the voltage at the clock signal input is higher than that at the data signal input.