****************************************************** PR # 41286 We propose an ASCA search for X-ray counterparts of the two very intense gamma-ray bursts, GRB930131 and GRB940217. GRB930131 displayed very strong peak intensity of 168 photons/cm2/sec which was the brightest one detected before with BATSE/CGRO. GRB940217 showed surprising characteristics; it lasted for more than 5,000 seconds in a band from several tens of MeV to about 18 GeV after the cessation of the lower energy busting activity < MeV. This is the most intense burst in a GeV range ever seen before. These two bursts, therefore, should be regarded as belonging to the nearest GRBs. Furthermore, they have both localized in small error regions. From these reasons, they should be the best targets for an X-ray counterpart search. ******************************************************