Using information-theoretic statistics, two series of substorm recurrence times are examined for evidence of dynamical structure. One series is from 1 year of energetic-electron data collected by geosynchronous satellites and the other series is from 8 years of the AL index. It is found that there is evidence for some predictive structure in these series; that is, the length of the time interval between two subsequent substorms depends on the previous intersubstorm interval length and that a large amount of the predictability can be attributed to roughly periodic substorms trains. ¿ American Geophysical Union 1996