Particle-injection events are monitored on three geosynchronous satellites to determine the occurrences of magnetospheric substorms: for every consecutive pair of substorms found, the time interval Δt between substorm onsets is determined. In this manner, 1001 values of Δt are obtained. A statistical analysis of the Δt values finds that the most-probable time between substorms onsets is Δt≈2.75 hours: this is interpreted to be the period between substorms when substorms occur cyclically. The statistical analysis of the Δt values also finds a random probability for the occurrence of substorms with a mean time between random substorms of about 5 hours: it is speculated that this random occurrence may be caused by a property of the solar wind that varies randomly with an approximately 5-hour time scale. About 1500 substorms occur per year: about half are periodic and about half occur randomly. ¿ American Geophysical Union 1993