  In a number of the most luminous ULXs (L ~ 1 E+40 erg/s) in nearby galaxies,
observations with XMM-Newton and Chandra are revealing evidence which suggests
that these ULXs may harbor intermediate-mass black holes (IMBHs). The detection
of accretion disk spectral components with temperatures 5-10 times lower than
the temperatures observed in stellar-mass black hole binaries near to their
Eddington limit may be particularly compelling evidence for IMBH primaries,
since T ~ M^(-1/4) for disks around black holes. In some sources, X-ray timing
diagnostics also hint at IMBHs. Evidence for IMBHs in a subset of the most
luminous ULXs, a discussion of the robustness of this evidence and alternatives
to the IMBH interpretation, and prospects for better determining the nature of
these sources in the future, are presented in this work.
