The purpose of this study is to understand the space density and properties of active galaxies to . We have invesz 0.8 tigated the frequency and nature of unresolved nuclei in galaxies at moderate redshift as indicators of nuclear activity such as active galactic nuclei (AGNs) or starbursts. Candidates are selected by fitting imaged galaxies with multicomponent models using maximum likelihood estimate techniques to determine the best model fit. We select those galaxies requiring an unresolved, point source component in the galaxy nucleus, in addition to a disk and/or bulge component, to adequately model the galaxy light. We have searched 70 WFPC2 images primarily from the Medium Deep Survey for galaxies containing compact nuclei. In our survey of 1033 galaxies, the fraction containing an unresolved nuclear component ≥3% of the total galaxy light is corrected for incompleteness. Most of the nuclei 16% 3% comprise less than 20% of the total galaxy light. The majority of the host galaxies are spirals with little or no bulge component having a distribution of Hubble types comparable to that for “dwarf” Seyfert nuclei in nearby galaxies (L. C. Ho, A. Fillipenko, & W. L. W. Sargent, ApJS, 112, 315 [1997]) and local starburst nuclei (V. Balzano, ApJ, 268, 602 [1983]). The colors of the nuclei are compared with synthetic colors V I for Seyferts and starburst nuclei to help differentiate between AGNs and starbursts in our sample. Spectroscopic redshifts have been obtained for 35 of our AGN/starburst candidates and photometric redshifts are estimated to an accuracy of for the remaining sample. j 0.1 z Figure 1 is the luminosity function for compact nuclei in our sample having colors consistent with those of Seyfert nuclei. This represents an upper limit LF for low-luminosity AGNs (LLAGNs) in two redshift bins to . We detect z 0.8 mild number density evolution of the form for 1.9 f ∝ (1 z) nuclei at . Our LF shows a smooth transition 18 M 14 B from the brighter Seyfert LF of J. Huchra and R. Burg (ApJ, 393, 90 [1992]) and flattens at . This flattening of M ≥ 16 B the LF at fainter magnitudes is inconsistent with models using pure luminosity or density evolution fitted to quasar LFs at similar redshifts. Based on the observed number density of compact nuclei in this study, we find that almost all presentday spiral galaxies may host an active LLAGN at some point in their lives.