The author considers two types of nonlinear, anisotropic, thermoelastic plate theories - the Timoshenko type and the Ambartsumyan type. Specifically, orthotropic plates are considered. Equilibrium equations are derived by the use of Lagrangian principle in both the theories. The nonlinearity in the differential quantities is introduced as a result of taking into account of the square and products of the angles of rotation of classical plate theory. The displacement fields introduced in the two theories differ from each other. The final equilibrium equations of the Ambartsumyan type are found to be of twelfth order, whereas equations of Timoshenko type are of tenth order. The author concludes after some discussion that the nonlinear equations and relations of the Ambartsumyan type offer the possibility of satisfying static conditions at plane surfaces which is evidently an advantage for the nonlinear theory in comparison with the Timoshenko equations. The author also extends his discussion to the flexure of an infinitely long, transversely isotropic plate.