The few strongest shocks within several seismo-volcanic crises of La Soufrière were recorded by the event-triggered seismograph DMD on Dominique Island. Two P-wave arrivals, attributable to different paths of propagation, may be distinguished. The time interval between them changed for successive strong shocks in each crisis. The constraint on focal coordinates given by the local array around La Soufrière allows an interpretation of these observations, together with others from the Guadeloupe and Martinique arrays, in terms of a migration of successive strong shocks during a crisis, probably in an upward direction. © 1979.