A model of liquid nanolayers is developed. The model takes into account an ability of a liquid in nano-clearances to accept anisotropy under action of a hydrodynamical stream, and also to borrow pseudo-crystal structure under action of a crystal substrate. Two fields are introduced: a field of macroscopic velocities V(r,t) and a field of micro-shifts u(r,t). The dissipative phenomena are described by the field V(r,t). The field u(r,t) describes the structural changes caused by displacement of neighboring atoms in short-range order domains. The fields V(r,t) and u(r,t) are found from two vector equations. The first equation is a generalization of the Navier-Stokes equation. The second equation is a generalization of the sine-Gordon equation. The steady-state (Couette and Poiseuille) flows of the structured liquid in a gap between parallel planes are considered. The analysis of solutions allows to establish distinctions in rheological properties of Newtonian and the structured liquids.