Approximations of classifications, introduced and studied by Grzymala Busse  is a notion different from the notion of approximations of sets (Pawlak ). In fact the equivalence classes of approximate classifications cannot be arbitrary sets. Busse  had established properties of approximations of classifications which were recently extended to necessary and sufficient type theorems by Tripathy et. al (). Four types of covering based rough sets have been obtained as generalization of basic rough sets. Also another covering rough set from a topological point of view has been obtained (14, 15, 16, 17, 18, 19]. Attempts have been made in  to extend the above results to covering based rough sets. In this paper we carry out this study further by deriving results for all the five types of covering based rough sets. These results can be used to derive rules for information systems with domains of attributes values being covers instead of partitions. Copyright © 2009 ACM.