Several papers (see [5], [6], [7] and [8]) gave necessary and sufficient conditions for UM to be a hereditary radical class if M is a class of rings satisfying various conditions. Analogous to the concepts of special classes and special radical classes in the case of supernilpotent radical classes, we will use some of the results from the above—mentioned papers to define the concepts of super classes and super radical classes in the case of subidempotent radical classes.