General equations are proposed to describe the simultaneous rotations of the magnetization vectors and the displacements of curved domain walls in one pair of magnetostatically coupled magnetic films separated by a variable distance. Leakage-field energy is written in the "transmission-line" approximation. The effects of dissipation and the constraint of flux continuity across a domain wall are handled by d'Alembert's virtual work principle. The result is a set of coupled equations of the following kinds: (1) dynamic torque balance at each point inside a domain, (2) wall-domain constraint due to flux continuity, (3) boundary condition on domain magnetization which depends on instantaneous wall positions, and (4) wall velocity. Within certain limitations these equations apply to the core of an inductive magnetic recording head.