Determination of a nonlinear system is more difficult than a linear system because of the requirement to reconstruct composed elements. The cochlea is a frequency analyzer in our ear and shows nonlinearities such as two-tone suppression (2TS) and distortion product (DP) for two tones. In the psychological and clinical studies, those nonlinearities have been also measured. However, accurate measurements are difficult. Because, it is unclear that 2TS and DP are depend on each other. Present paper proposes a nonlinear model of the cochlea to investigate underlying mechanisms of 2TS and DP. The nonlinear element in the model is based on assumptions from the physiological features of the outer hair cell (OHC) in which unity decides nonlinearity of the cochlear model. The OHC's input-output function is saturating characteristic derived from mechano-electro transduction at the apex of OHC. To extend this one-dimensional property to two-dimensional property, the OHC model shows DP and 2TS. The cochlear simulation result is also similar to the OHC result. Two-tone produces DP at equaled levels of two-tones and 2TS where levels of two-tones differ. These results suggest that DP and 2TS in the cochlea can be explained by the two dimensional property in the OHC. Furthermore, in psychological and clinical measurements, they may not interact with each other.