One- and two-photon absorption spectra (OPA and TPA) and polarizabilities of ethylene, trans-butadiene, trans-hexatriene, and trans-octatetraene are investigated by means of linear and quadratic response theory calculations. It is demonstrated that accurate results for the one-photon excitation spectra of these short polyenes can be obtained already at the lowest level of response theory, namely, the random phase approximation (RPA). The excellent agreement with the experimental one-photon spectra generally within one or two tenths of an electronvolt, indicates that the comparatively simple but still well-defined RPA method has important ramifications for the study of linear optical properties of the conjugated polyenes. The polarizabilities generated by RPA are within a few percent of the vapor-phase values at the corresponding frequencies. Two-photon spectra of the short polyenes are investigated by the quadratic RPA method. Two-photon absorption maxima have been found for the even states of trans-butadiene, trans-hexatriene, and trans-octatetraene located at 1.5-1.7 Eg. The first one-photon forbidden (1)A(g) state is found to have a very small two-photon amplitude and is therefore likely not to contribute significantly to the nonlinear properties of the polyenes, although it might intrude the one-photon bandgap. The mechanism of optical nonlinearity in the short conjugated polyenes is explored in relation to the so-called three- and four-state models. It is found that the validity of these models for calculations of hyperpolarizabilities of the short polyenes is rather limited.