This is the abstract of the paper "Characteristic Equations for the Spectrum of Generators" by Rainer Nagel. For the whole paper send the command get evolve-l 97-00027 to: listserv@rz.uni-karlsruhe.de Instead you may get the paper at "http://www.uni-karlsruhe.de/~listserv/archive/EVOLVE-L.html" too. Abstract: We propose an abstract framework for the computation of the spectrum $\sigma(A)$ of a linear operator $A:D(A)\subset X\to X$ on a Banach space $X$ through a condition in a smaller Banach space $X_1$. If this space is finite dimensional this yields a characteristic equation for $\sigma(A)$. The method is tested for delay, integro-differential and population equations and is applicable to control and stability questions.