The linear, normal mode instability of three-dimensional laminar and turbulent shear layers is studied. The flows consist of two streams semi-infinitely extended in the y-direction, flowing obliquely in the x-z plane. It is found that the stability of the flows depends on the main flow velocity components in the direction of the disturbance wave-number vector. Numerical calculations are performed to obtain the neutral stability curves. Under the usual parallel unperturbed flow assumption, the neutral stability curves pass through the origin of the α-R diagram, where α is the wave-number and R is the flow Reynolds number. It is also found that eddy viscosity has a destabilizing effect for small Reynolds numbers but a stabilizing effect at larger Reynolds numbers. Because any linear perturbation trajectory eventually leaves the unstable region of the α-R plane, it is probable that a Lin-Benney or Taylor-Goertler secondary instability ensues. Suitable components of the existing turbulence grow and develop into a large eddy system which causes rapid entrainment, giving rise to a turbulent burst. A first-order non-parallel correction is made to the neutral stability curves. The new curves have both upper and lower branches, and there exist minimum critical Reynolds numbers.