************************************************************************* 61178 The catalog of Shakhbazyan's compact groups of galaxies (SCGGs) is a catalog that has never been explored in X-rays in the past. We propose ASCA observations on two representative compact groups (SCGG 205 and SCGG 223) from this catalog. Each target consists of about ten member galaxies and shows extremely large velocity dispersion ($>1000$ km s$^{-1}$). By measuring the total gravitating mass, together with temperature and abundance of the intra-group gas, we expect new breakthroughs on the study of groups and clusters of galaxies. *************************************************************************