A capacitive proximity sensor for use in mobile devices such as smartphones and connected tables, in which it is used to switch off a display (70) when the device is brought to the ear. The capacitive sensor is arranged for rejecting spurious detection induced, for example, by condensation, ingress of water, or thermal drift, based on the time variations of a capacity seen by the readout circuit (80), Additionally, the proximity sensor may integrate signals form motion sensors, temperature sensors or other sensors, to discriminate spurious proximity signals.