We show how to extend the 't Hooft anomaly matching conditions to discrete
symmetries. We check these discrete anomaly matching conditions on several
proposed low-energy spectra of certain strongly interacting gauge theories. The
excluded examples include the proposed chirally symmetric vacuum of pure N=1
supersymmetric Yang-Mills theories, certain non-supersymmetric confining
theories and some self-dual N=1 supersymmetric theories based on exceptional
groups.Comment: 6 pages, LaTeX. Talk presented by Csaba Csaki at the XXXIIIrd
Rencontres de Moriond, Electroweak Interactions and Unified Theories, Les
Arcs, Savoie, France, March 14-21, 199
