  We report experimental observation of an instability in a Couette-Taylor flow
of a polymer fluid in a thin gap between two coaxially rotating cylinders in a
regime where their angular velocity decreases with the radius while the
specific angular momentum increases with the radius. In the considered regime,
neither the inertial Rayleigh instability nor the purely elastic instability
are possible. We propose that the observed "elasto-rotational" instability is
an analog of the magnetorotational instability which plays a fundamental role
in astrophysical Keplerian accretion disks.
