The linear regime (LR) of viscoelastic behavior has been found to be limited to rather small values of strain, well below the strains found in many technological processes. A Fourier-transform method is described for analyzing the surface rheology data obtained in insoluble Langmuir polymer monolayers beyond the LR. In the concentrate regime, the monolayers show a transition from elastic to plastic behavior, which is characterized by high irreversibility. A simple 2-D rubber model is presented that describes the behavior of the monolayers in the non-linear region not too far from the end of the LR.