An event-monitoring system including saturable core devices having respective separate saturable cores most desirably each carrying a biasing winding and a scanning winding, the biasing windings being connected in series with one another and the scanning windings being connected in series with one another. The biasing windings of the saturable core devices have different numbers of turns so an instantaneous predetermined magnitude of biasing current will saturate the cores to progressively increasing degrees. The series connected scanning windings receive a scanning current of progressively increasing value, which most advantageously have an AC component superimposed thereon, to develop an oppositely directed progressively increasing electromagnetic field sequentially to unsaturate the cores at predetermined current values normally to cause sequential electrical output signals to be generated thereby, the interval during which unsaturation occurs being a large number of cycles at the modulating frequency. Associated conditionresponsive switch means are connected to each saturable core device, such as across each scanning windings, or preferably across a separate isolation winding, so closure of the switch means will prevent the generation of said output signal.