  We continue to investigate the X-ray timing and spectral properties of the
black hole binary, XTE J1550-564. For three different groups of observations,
we show evidence that two high-frequency QPOs (HFQPOs) occur simultaneously
near 184 and 276 Hz. In one group, there is also evidence of a broad feature at
92 Hz. In each case, we can model the QPO profiles while assuming that the
central frequencies are related as integral harmonics of a single frequency. We
next investigate the X-ray energy spectra, and we find a systematic increase in
the strength of the power-law component as the stronger of the two HFQPOs
shifts from 276 to 184 Hz. A strikingly similar result is seen for GRO J1655-40
when the stronger HFQPO shifts from 450 to 300 Hz. The fundamental HFQPO
frequencies for the two X-ray sources scale inversely with black hole mass,
which is consistent with the hypotheses that these HFQPOs represent some
oscillation rooted in general relativity (GR) and that the two black holes have
similar values of the dimensionless spin parameter. We discuss physical
mechanisms that may explain these HFQPOs. In particular, a resonance between
the orbital and radial coordinate frequencies in the innner accretion disk, as
proposed by Abramowicz & Kluzniak, would imply moderate values for the
dimensionless spin parameter (0.1 < a < 0.6) for both black holes.
