A theoretical description of the propagation of an initially Gaussian beam through a “generalized” thin nonlinear medium is developed, where the linear part of the optical system can be characterized by an ABCD matrix. The optical field is determined on the output interface of the medium and is decomposed into Gaussian-Laguerre modes. These modes are then propagated through the optical system using the ABCD law, so that the field distribution at any point can be determined. We obtain an expression for the on-axis relative transmissivity of the combined system, which is valid for nonlinear absorption regimes to all orders of nonlinearity. The positions of the turning points of the normalized axial transmissivity as a function of the position of the medium are derived analytically to the first-order of nonlinearity. It is shown that, from measurements of these positions, the nonlinear refractive and absorptive strengths as well as the type of nonlinearity can be extracted.