We present spectroscopic observations of six optical counterparts of ultraluminous X-ray sources (ULXs) around nearby galaxies. The spectra of the six objects show the presence of broad emission features. The identification of these allow us to classify all of the objects as quasars at higher redshift than their assigned parent galaxy. This is one of the first and largest identifications of such objects using unambigous optical spectral features. These results, in conjuction with previous similar identifications of other sources, indicate that high-redshift quasars represent an important fraction of cataloged ULX sources. We estimate the density of such sources and compare this with expectations for a population of randomly distributed background quasars.