Multiple detectors giving nearly complete 4&pgr; coverage of particle pitch angle distributions have provided high resolution measurements (in energy and time) of 30- to 300-keV electrons. Data from a spacecraft (1976-059A) in geostationary orbit show a remarkably consistent sequence of variations of the electron anisotropy before and during magnetospheric substorms. For periods typically 1--2 hours prior to the onset of substorms, electron distributions, peaked along the direction of the local magnetic field, are observed in the premidnight sector. These cigarlike anisotropies are accompanied by a local taillike magnetic field which may develop further during the event. At substorm onset an abrupt transition usually occurs from the cigar-shaped distributions to pancake-shaped distributions. This anisotropy sequence may be due to the buildup and subsequent release of stresses in the magnetotail; the cigar phase may also be due to associated processes at the dayside magnetopause causing a loss of 90¿ pitch angle particles. The present observations, based on ~100 events, appear to provide a predictive tool for assessing the probability of occurrence of a substorm.