In the large solar energetic particle (SEP) events that constitute a serious radiation hazard, particles are accelerated at shock waves driven out from the Sun by coronal mass ejections (CMEs). A self-regulating mechanism of wave formation by the streaming particles limits SEP intensities early in the event. Hazardous intensities do not occur until the arrival of the shock itself. This provides an opportunity to warn astronauts to take shelter after the onset of the event at the Sun and before arrival of the shock, a time of similar to 12 h or more. The actual time history of particle intensities depends strongly. on the longitude of the event at the Sun, on the width the CME, and especially on the speed of the shock. Fortunately, hazardous events are relatively rare. Unfortunately, this gives us few events to study, so we are forced to extrapolate knowledge gained at lower energies in the frequent smaller events. It is essential that the spacecraft with our best instrumentation be positioned outside the Earth's magnetosphere where they can observe these rare large events when they do occur. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.