We report on the nonlinear optical properties measurements and quantum-chemical calculations of a well-known photochromic system consisting of spiropyran and the merocyanine photoproduct. The study of nonlinear absorption and refraction properties of the molecules dissolved in chloroform were performed with the Z-scan technique, using femtosecond pulses, in a wide range of the wavelengths. Maxima in the two-photon absorption spectrum at 700 nm and 1050 nm are found for the merocyanine form and the corresponding two-photon absorption cross section is 80 GM and 20 GM, respectively. The latter feature does not vanish completely in the nonlinear spectrum of the spiropyran form, possibly due to the existence of some photoconversion caused by the laser beam during the measurements. A nonlinear absorption peak at 900 nm is found in the spiropyran form with the effective cross section about 20 GM; it is likely to be due to three-photon absorption or to absorption by some intermediate species. The experimental data are supported by calculations performed with the use of a hybrid quantum mechanics/molecular mechanics approach.