The paper presents a computational investigation of instabilities in pulsatile flow through a three-dimensional stenosis. The computations have been conducted using a third-order high-resolution scheme and a non-linear multigrid algorithm. The simulations reveal the existence of unstable flow throughout the pulsatile cycle. The instability is manifested by asymmetric flow patterns - though the stenosis is axisymmetric-large flow variations in the cross-sectional planes, and swirling motion in the poststenotic region. The instability leads to a strongly disturbed flow several radii downstream of the stenosis, as well as spatio-temporal fluctuations of the circumferential shear stress and vorticity.