We have studied competitive optical nonlinearities - excited state absorption (ESA), absorption saturation (SA) and two-photon absorption (TPA) - of epoxy polymer based on diglicidyl ether of bisphenol A with picosecond Z-scan technique at 532 nm. The complexity of the analysis was dealt with problem of the selection of the part of Z-scan curve which corresponds to the dominant contribution of the proper nonlinear mechanism on the background of competitive others. The TPA coefficient is beta =4.0 +/-0.5 cm/GW for the polymer. At high laser intensities (>7 GW/cm(2)) photoinduced transformation into some new configuration is taken place that is more absorbent at 532 nm (beta =16.7 +/-3 cm/GW for the photoproduct). Up to a pumping irradiance of 20 GW/cm(2) no optical damage of the polymer was observed.