Electron parallel dynamics and Coulomb collisions are included in the analysis of the transverse Kelvin-Helmholtz instability. The electrons are treated kinetically while the ions are treated in the fluid limit. It is shown that in the collisionless case, for an imhomogeneous velocity profile V(x)=V0 tanh (x/L) the Kelvin-Helmholtz instability is stable for kz/ky>(V0/L&ohgr;lh)KyL [2(1-ky2L2)>1/2 in the limit &ohgr;-kyV0≫kzve. Here V0 is the flow velocity, L is the scale length of the velocity shear layer, kz and ky are the parallel and perpendicular wave numbers, respectively, &ohgr;lh=(&OHgr;e&OHgr;i)1/2, and ve is the electron thermal velocity. The stabilization of the mode is shown to be caused by the compressional energy given to the electrons parallel to B. In the collisional limit, Coulomb collisions are shown to increase the unstable kz domain becasue they inhibit the electron motion parallel to B. Applications to the high-latitude ionosphere are discussed. ¿ American Geophysical Union 1987