The Hubble Space Telescope WFPC2 is being used to obtain high-resolution images in the V and I bands for several thousand distant galaxies as part of the Medium Deep Survey (MDS). An important scientific aim of the MDS is to identify possible AGN candidates from these images in order to measure the faint end of the AGN luminosity function as well as to study the host galaxies of AGNs and nuclear starburst systems. We are able to identify candidate objects based on morphology. Candidates are selected by fitting bulge+disk models and bulge+disk+point source nuclei models to HST imaged galaxies and determining the best model fit to the galaxy light profile. We present results from a sample of MDS galaxies with I less than 21.5 mag that have been searched for AGN/starburst nuclei in this manner. We identify 84 candidates with unresolved nuclei in a sample of 825 galaxies. For the expected range of galaxy redshifts, all normal bulges are resolved. Most of the candidates are found in galaxies displaying exponential disks with some containing an additional bulge component. 5% of the hosts are dominated by an r^-1/4 bulge. The V-I color distribution of the nuclei is consistent with a dominant population of Seyfert-type nuclei combined with an additional population of starbursts. Our results suggest that 10% +/- 1% of field galaxies at z less than 0.6 may contain AGN/starburst nuclei that are 1 to 5 magnitudes fainter than the host galaxies.

12 pages AASTeX manuscript, 3 separate Postscript figures, to be published in ApJ Letters