The existence of either pre- or post-burst emission can provide substa
ntial new information about the burst source and its local environment
. We have data from several events serendipitously in or near the OSSE
field of view at the time of the burst. We present pre- and post-burs
t flux limits from one such event, GRB 940301. The OSSE data for other
periods when scheduled observations have included burst locations wil
l enable us to search for pre- and post- burst emission on many time s
cales.