  We study the homogeneous and the spatially periodic instabilities in a
nematic liquid crystal layer subjected to steady plane {\em Couette} or {\em
Poiseuille} flow. The initial director orientation is perpendicular to the flow
plane. Weak anchoring at the confining plates and the influence of the external
{\em electric} and/or {\em magnetic} field are taken into account. Approximate
expressions for the critical shear rate are presented and compared with
semi-analytical solutions in case of Couette flow and numerical solutions of
the full set of nematodynamic equations for Poiseuille flow. In particular the
dependence of the type of instability and the threshold on the azimuthal and
the polar anchoring strength and external fields is analysed.
