Linear stability of two-dimensional flows in a frame rotating with angular velocity vector&OHgr;=&OHgr;ezperpendicular to their plane is considered. Sufficient conditions for instability have been derived for simple inviscid flows, namely parallel shear flows (characterized by the “Pedley” or “Bradshaw-Richardson” number), circular vortices (by the “generalized Rayleigh” discriminant) and unbounded flows having a quadratic streamfunction (with elliptical, rectilinear or hyperbolic streamlines). These exact criteria are reviewed and contrasted using stability analysis for both three-dimensional disturbances and oversimplified “pressureless” versions of the linear theory. These suggest that one defines a general inviscid criterion for rotation and curvature, based on the sign of the second invariant of the “inertial tensor,” and stating that, in a Cartesian coordinate frame:a sufficient condition for instability is that&Fgr;(x,y)=−12S:S+14Wt⋅Wt<0somewhere in the flow domain.It involves the “tilting vorticity”Wt=W+4&OHgr;[Cambon &etal;, J. Fluid Mech.278,175 (1994)] and the symmetric partSof the velocity gradient of the basic flow. ©1997 American Institute of Physics.