We examine the stability of sheared flows in an inversely stratified fluid (where the density increases upward). As demonstrated by Kuo (1963), if the shear and Vasala frequency are both constant (i.e., if the velocity and density profiles are both linear), the shear suppresses the Rayleigh-Taylor instability that would affect the fluid in the absence of the flow. Our main goal is to reexamine this problem for a wider class of velocity and density profiles. Using the standard linear normal-mode analysis, we consider two types of flows: jets (for which asymptotic solutions were found), and currents with a monotonic profile (which were examined numerically). It turns out that virtually any deviation from the linear profiles examined by Kuo (1963) triggers off instability. This instability, however, is restricted either spectrally or spatially, which makes it different from the usual Rayleigh-Taylor instability (in the absence of the flow, inversely stratified fluids are unstable at all points and all wavelengths). The conclusions of the paper are verified by simulation of the governing (nonlinear) equations. (C) 2002 American Institute of Physics.