We have developed a one-dimensional, diurnally averaged, photochemical model for Jupiter's stratosphere that couples photodissociation, chemical kinetics, vertical diffusion, and radiative transport. The predictions regarding the abundances and vertical profiles of hydrocarbon compounds are compared with observations from the Infrared Space Observatory (ISO) to better constrain the atmospheric composition, to better define the eddy diffusion coefficient profile, and to better understand the chemical reaction schemes that produce and destroy the observed constituents. From model-data comparisons we determine that the C2H6 mole fraction on Jupiter is (4.0 ¿ 1.0) ¿ 10-6 at 3.5 mbar and (2.7 ¿ 0.7) ¿ 10-6 at 7 mbar, and the C2H2 mole fraction is (1.4 ¿ 0.8) ¿ 10-6 at 0.25 mbar and (1.5 ¿ 0.4) ¿ 10-7 at 2 mbar. The column densities of CH3C2H and C6H6 are (1.5 ¿ 0.4) ¿ 1015 cm-2 and (8.0 ¿ 2) ¿ 1014 cm-2, respectively, above 30 mbar. Using identical reaction lists, we also have developed photochemical models for Saturn, Uranus, and Neptune. Although the models provide good first-order predictions of hydrocarbon abundances on the giant planets, our current chemical reaction schemes do not reproduce the relative abundances of C2Hx hydrocarbons. Unsaturated hydrocarbons like C2H4 and C2H2 appear to be converted to saturated hydrocarbons like C2H6 more effectively on Jupiter than on the other giant planets, more effectively than is predicted by the models. Further progress in our understanding of photochemistry at low temperatures and low pressures in hydrogen-dominated atmospheres hinges on the acquisition of high-quality kinetics data.