The transition of LCPs textures, initiated by shear flow and stipulated by elastic and dissipative properties are analyzed. Loss of the texture stability for nematics in the flow of LCPs is realised in the range of shear rate within lim n||'(w,q0); lim G||'(w,q0)/w2 and lim Gt'(w,q0)/w2 (w->0) are negative. The problem of parallel and orthogonal superposition of steady flow and small amplitude oscillatory shear is solved for the Akay-Leslie anisotropic nonlinear viscoelastic liquid. Two regions of the flow instability are cited: the first one, named textural, at low shear rates and the second, a viscoelastic one, which is inherent also for flexible chain polymers. Test data show a qualitative agreement between the calculations and experiments. A quantitative agreement requires a generalization of the model on a spectrum of the relaxation times.