************************************************************************* 51268 In spite of the extensive efforts by many observers, classical gamma- ray bursts (GRBs) is remained unexplained for more than 25 years. The previous ASCA X-ray counterpart searches of GRBs have revealed X-ray sources in the small errors of GRB 781119 and 920501. Because of the low probabilities finding an X-ray source by chance in such small errors, this strongly suggests the real counterpart of the GRBs. However, number of examples is very much limited of only two and also the observations were done based on some selection bias, tracing the existing results of the Einstein and the ROSAT. So, we are proposing more unbiased, deep general survey of GRB errors in search for an X-ray counterpart. *************************************************************************