This is the abstract of the paper "On the Regularity Properties of Perturbed Semigroups" by Rainer Nagel and Susanna Piazzera. For the whole paper send the command get evolve-l 98-00031 to: "listserv@rz.uni-karlsruhe.de". Instead you may get the paper at "http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html" too. Abstract: We give conditions on a strongly continuous semigroup $T$ and a bounded operator $B$, such that the perturbed semigroup inherits the regularity properties of $T$.