This is the abstract of the paper "Spectral inclusions for semigroups of closed operators" by Peer Christian Kunstmann. For the whole paper send the command get evolve-l 99-00094 to: "listserv@uni-karlsruhe.de". Instead you may get the paper at "http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html" too. Abstract: We show that several spectral inclusions known for $C_0$-semigroups fail for semigroups of closed operators, even if they can be regularized. We introduce the notion of spectral completeness for the regularizing operator $C$ which implies equality of the spectrum and the $C$-spectrum of the generator. We prove spectral inclusions under this additional assumption. We give a series of examples in which the regularizing operator is spectrally complete including generators of integrated semigroups, of distribution semigroups, and of some semigroups that are strongly continuous for $t>0$.