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 C₂H _x 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.