The nonlinear optical characteristics of some organic materials namely coumarin derivatives [3-[(2E)-3-phenylprop-2-enoyl]-2H-chromen-2-one(Cm1) and 3-{(2E)-3-[4-(dimethylamino)phenyl]prop-2-enoyl}-2H-chromen-2-one (Cm2)] doped in a polymer matrix of polymethylmethacrylate (PMMA) have been studied. The Z-scan study on these composite films reveals that the compounds exhibit a self-focusing effect at 532 nm. The nonlinear absorption coefficient, nonlinear refractive index and second-order molecular hyperpolarizability are measured. The optical power limiting experiment is carried out and it is attributed to reverse saturable absorption due to excited state absorption in the samples. This article also reports the enhancement of third-order nonlinearity by substituting with an electron donor group and hence establishes the electronic nature of nonlinearity. (C) 2011 Elsevier B.V. All rights reserved.