Intensity-dependent characteristics for TM-polarized optical waves guided by multiple-quantum-well (MQW) waveguides with arbitrary nonlinear media are numerically analyzed by the finite element method. In this approach, self-consistent solutions are obtained through a simple iterative procedure. The power-dependent dispersion relations and magnetic-field (H(x)) as well as two electric-field (E(y) and E(z)) profiles for nonlinear TM waves in MQW waveguides with three different nonlinear mechanisms are presented. It is shown that, for the waveguides with molecular orientational mechanism, a distinct power limiting action for nonlinear TM modes exists.