  We present the preliminary results of two Gemini campaigns to constrain the
mass of the black hole in an ultraluminous X-ray source (ULX) via optical
spectroscopy. Pilot studies of the optical counterparts of a number of ULXs
revealed two candidates for further detailed study, based on the presence of a
broad He II 4686 Angstrom emission line. A sequence of 10 long-slit spectra
were obtained for each object, and the velocity shift of the ULX counterpart
measured. Although radial velocity variations are observed, they are not
sinusoidal, and no mass function is obtained. However, the broad He II line is
highly variable on timescales shorter than a day. If associated with the
reprocessing of X-rays in the accretion disc, its breadth implies that the disc
must be close to face-on.
