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A system of approximate two‐dimensional surface‐wave equations and edge conditions in one scalar variable is derived from Hamilton's principle for linear piezoelectric media by assuming suitable depth behavior and integrating with respect to depth. The assumed behavior with depth is determined from the known straight‐crested surface‐wave solutions of the three‐dimensional equations for the plated and unplated substrate in connection with the known variable‐crested solutions for the isotropic substrate. The influence of the inertia, stiffness, and electrical shorting of the film is included in the analysis. The application of the derived equations to the problems for isotropic substrates treated earlier by an ad hoc technique indicates that the derived equations are extremely accurate. Among other things, the analysis reveals that a slot in an aluminum‐oxide film on a T‐40 glass substrate exhibits guiding characteristics twice as good as the combination of aluminum on T‐40 glass in the essentially nondispersive range. The derived equations are used in the determination of the dispersion curves for piezoelectric surface waves guided by gold strips on y‐cut lithium niobate for propagation in the x and z directions, respectively. Although the dispersion curves for z propagation turn out as expected, the dispersion curves for x propagation have an interesting and unusual shape indicating two ranges of essentially nondispersive propagation. The unusual shape is a consequence of the fact that two straight‐crested surface waves couple strongly in the propagation range of interest.