We present a search for the production of excited or exotic muons
(mu*) via the reaction pbar + p --> mu* + mu --> mu gamma + mu using 371
pb-1 of data collected with the Run II CDF detector.  In this
signature-based search, we look for a resonance in the mu gamma mass
spectrum.  The data are compared to standard model and detector background
expectations, and with predictions of excited muon production.  We use these
comparisons to set limits on the mu* mass and compositeness scale Lambda in
contact interaction and gauge-mediated models.