Search for Exotic and Excited Muons at CDF We search for the production of excited or exotic muons (mu*) via the reaction $p\bar{p} \rightarrow \mu^* + \mu \rightarrow \mu \gamma + \mu$ using 371 pb$^{-1}$ of data collected with the Run 2 CDF detector. This signature based search looks for a resonance in the mu-gamma mass spectra that would indicate a discovery outside the Standard Model. The data are compared with Standard Model expectations and detector backgrounds, and with predictions of excited muon models. We use these comparisons to set limits on the mu* mass and compositeness scale in a Contact Interaction and Gauge Mediated model.