  We study galaxies that host both nuclear star clusters and active galactic
nuclei (AGN) implying the presence of a massive black hole. We select a sample
of 176 galaxies with previously detected nuclear star clusters that range from
ellipticals to late-type spirals. We search for AGN in this sample using
optical spectroscopy and archival radio and X-ray data. We find galaxies of all
Hubble types and with a wide range of masses (10^9-11 solar masses) hosting
both AGN and nuclear star clusters. From the optical spectra, we classify 10%
of the galaxies as AGN and an additional 15% as composite, indicating a mix of
AGN and star-formation spectra. The fraction of nucleated galaxies with AGN
increases strongly as a function of galaxy and nuclear star cluster mass. For
galaxies with both a NC and a black hole, we find that the masses of these two
objects are quite similar. However, non-detections of black holes in Local
Group nuclear star clusters show that not all clusters host black holes of
similar masses. We discuss the implications of our results for the formation of
nuclear star clusters and massive black holes.
