  We derive the locations of the fully synchronous end states of tidal
evolution for binary asteroid systems having one spherical component and one
oblate- or prolate-spheroid component. Departures from a spherical shape, at
levels observed among binary asteroids, can result in the lack of a stable
tidal end state for particular combinations of the system mass fraction and
angular momentum, in which case the binary must collapse to contact. We
illustrate our analytical results with near-Earth asteroids (8567) 1996 HW1,
(66391) 1999 KW4, and 69230 Hermes.
