Strong nonlinear absorption is observed in nanocomposite films containing PbS nanocrystals of mean size of 3.3 nm stabilized in a commercial poly(vinyl acetate) glue by a novel and simple chemical route of synthesis. A significant blueshift of the optical absorption edge indicates strong quantum confinement. The mean nanocrystal size was characterized by x-ray diffraction and transmission electron microscopy. The surface structure of nanocrystals is analysed using infrared spectroscopy. The excitonic transitions are probed by photoacoustic spectroscopy and the results are analysed on the basis of theoretical calculations using envelope function formalism. Results of open aperture z-scan experiments suggest a model involving saturable absorption followed by two-photon absorption at a lower concentration while the data for a higher concentration fitted saturable absorption followed by three-photon absorption. Free carrier absorption due to two-photon-assisted excited state absorption appears to be the predominant mechanism of optical nonlinearity.