  We investigate the equilibrium and stability of supermassive stars of mass $M
\agt 10^5M_{\odot}$ in binary systems. We find that corotating binaries are
secularly unstable for close, circular orbits with $r \alt
4R(M/10^6M_{\odot})^{1/6}$ where $r$ is the orbital separation and $R$ the
stellar radius. We also show that corotation cannot be achieved for distant
orbits with $r \agt 12 R (M/10^6M_{\odot})^{-11/24}$, since the timescale for
viscous angular momentum transfer associated with tidal torques is longer than
the evolution timescale due to emission of thermal radiation. These facts
suggest that the allowed mass range and orbital separation for corotating
supermassive binary stars is severely restricted. In particular, for
supermassive binary stars of large mass $M \agt 6\times 10^6M_{\odot}$,
corotation cannot be achieved, as viscosity is not adequate to mediate the
transfer between orbital and spin angular momentum. One possible outcome for
binary supermassive stars is the onset of quasi-radial, relativistic
instability which drives each star to collapse prior to merger: We discuss
alternative outcomes of collapse and possible spin states of the resulting
black holes. We estimate the frequency and amplitude of gravitational waves
emitted during several inspiral and collapse scenarios.
