We prove that every one dimensional extension of a separably acting normal operator has a cyclic commutant, and that every non-algebraic normal operator has a two-dimensional extension which fails to have a cyclic commutant. Contrasting this, we prove that if T is an extension of a normal operator by an algebraic operator then the weakly closed algebra W(T) has a separating vector. 1994 Birkhuser Verlag.
