The large-amplitude nonlinear shear theology of polymer melts confined between strongly adsorbing surfaces (parallel plates of mica) was studied as a function of strain, frequency, and thickness of the polymer films. The shear strains varied from less than 0.1 (linear response) to over 30 (at which the film structure was strongly modified by the imposed shear). The measurements employed a surface forces apparatus modified for dynamic mechanical shear. The polymers were atactic poly( phenylmethylsiloxane) (PPMS), with chain lengths from 31 to 153 skeletal bonds. The nonlinear shear forces, decomposed into a Fourier series of harmonic frequencies, were always odd in the excitation frequency, as required by symmetry considerations. The in-phase and out-of-phase oscillatory shear responses at the same frequency as the excitation (the nonlinear storage and loss moduli G(1)’ and G(1)", respectively) were analyzed. Four principal conclusions emerged. First, from the frequency dependence of G(1)’ and G(1)" at constant strain, we conclude that relaxations were accelerated by large strain. Second, a marked decrease of both G(1)’ and G(1)" was observed with increasing strain at constant frequency, except at the smallest film thickness, approximate to 40 Angstrom where G(1)" passed through a maximum with increasing strain but G(1)’ continued to display shear-thinning. Third, the critical strain for onset of nonlinear response increased with the excitation frequency. Fourth, at sufficiently large strains (larger than 10), the shear moduli were independent of polymer molecular weight (comparisons made at fixed film thickness) and appeared to reach limiting strain-independent levels at sufficiently large strains. This final observation contrasts sharply with the linear response and is consistent with shear-induced loss of interdigitation between opposed adsorbed polymer layers, consistent with the tendency toward slippage of adsorbed polymer layers over one another.