CMOS integrated circuits with very low consumption when idle, and notably the SRAM volatile memories, are provided. The inverters of the circuit are made up of an NMOS transistor and a PMOS transistor. A bias circuit applies a first rear bias voltage NBIAS to the wells of the NMOS transistors and a second rear bias voltage PBIAS to the wells of the PMOS transistors. The bias circuit comprises: a detection array made up of many inverters in parallel, having a common output supplying a logic signal whose value depends on the rear bias voltages applied to the array, a circuit for producing incrementation or decrementation pulses, controlled by the output of the detection array, and an integration circuit linked to the pulse-producing circuit, for producing and varying, progressively by increments in response to these pulses, a bias voltage PBIAS and a bias voltage NBIAS.