Abstract. Significant variations of the Earth's magnetic field seem to be associated with geodynamie phenomena, particularly volcanic eruptions and earthquakes. The variations have small amplitudes, generally only a few nT. These small signals are embedded into larger transient variations due to other natural or artificial causes. An original method of recovering interesting signals having amplitudes down to 1 nT, is to describe the whole variation analytically so that each component may be isolated. Several studies have shown that significant signals exist for tectonically active regions: 10-30 nT for large-scale arrays over periods of years; 5-15 nT for volcanic phenomena; 1-5 nT for earthquakes.Only a few test sites for volcanoes (New Zealand, Hawaii, Antilles) and earthquakes (essentially the San Andreas fault system) have been monitored so far.The cause of the type of magnetic variations studied here, which are associated with volcanism and rock failures, has most often been attributed to piezomagnetism. Some authors have suggested that electrokinetic effects associated with porosity-changes may also play a role.The isolated signals may, in the future, be used for hazard forecasting when the time-constants associated with the effects are known more precisely.