****************************************************** PR # 21128 Mkn 421 is one of the most interesting BL Lac objects: not only it is one of the GeV gamma-ray emitters discoverd by EGRET but also it is the only extra- galactic TeV gamma-ray emitter so far observed by Whipple Telescope. The spectrum in X-ray region shows the spectral breaks which are interpreted as a synchrotron cooling effect.However, it is hard to explain both GeV and TeV emission in the standard theor etical model(SSC) of the BL Lac objects. We thus propose this observa tion as a time critical observation with the EGRET GeV observation on May 10-16th, 1994. We will attempt to coordinate with the Whipple tel escope for the TeV observation, as well. This concurrent observation will give us crucial information to connect X-ray to GeV/TeV gamma- ray. ******************************************************