The influence of plasma and magnetic field gradients on the Kelvin-Helmholtz instability is investigated. The instability is driven by a sheared ion velocity flow parallel to the magnetic field. The modes considered satisfy k2L2≫1, where k is the wave number and L is the scale length of the inhomogeneity. It is found that a density gradient has a stablizing effect, while a temperature gradient has a destabilizing effect on the fastest growing mode. However, both these influence are relatively weak. More important, it is found that a magnetic field gradient is strongly stabilizing in finite &bgr; plasmas because of an ion ∇B drift wave resonance.