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Thermochemical equilibrium and kinetic calculations are used to model sulfur and phosphorus chemistry in giant planets, brown dwarfs, and extrasolar giant planets (EGPs). The chemical behavior of individual S-and P-bearing gases and condensates is determined as a function of pressure, temperature, and metallicity. The results are independent of particular model atmospheres and, in principle, the equilibrium composition along the pressure-temperature profile of any object can be determined. Hydrogen sulfide (H 2 S) is the dominant S-bearing gas throughout substellar atmospheres and approximately represents the atmospheric sulfur inventory. Silicon sulfide (SiS) is a potential tracer of weather in substellar atmospheres. Disequilibrium abundances of phosphine (PH 3 ) approximately representative of the total atmospheric phosphorus inventory are expected to be mixed upward into the observable atmospheres of giant planets and T dwarfs. In hotter objects, several P-bearing gases (e.g., P 2 , PH 3 , PH 2 , PH, HCP) become increasingly important at high temperatures.Subject headings: astrochemistry -planets and satellites: individual (Jupiter) -stars: low-mass, brown dwarfs -stars: individual (Gliese 229B, HD 209458)