We used one-dimensional photochemical and radiative transfer models to study the potential of organic sulfur compounds (CS(2), OCS, CH(3)SH, CH(3)SCH(3), and CH(3)S(2)CH(3)) to act as remotely detectable biosignatures in anoxic exoplanetary atmospheres. Concentrations of organic sulfur gases were predicted for various biogenic sulfur fluxes into anoxic atmospheres and were found to increase with decreasing UV fluxes. Dimethyl sulfide (CH(3)SCH(3), or DMS) and dimethyl disulfide (CH(3)S(2)CH(3), or DMDS) concentrations could increase to remotely detectable levels, but only in cases of extremely low UV fluxes, which may occur in the habitable zone of an inactive M dwarf. The most detectable feature of organic sulfur gases is an indirect one that results from an increase in ethane (C(2)H(6)) over that which would be predicted based on the planet's methane (CH(4)) concentration. Thus, a characterization mission could detect these organic sulfur gases-and therefore the life that produces them-if it could sufficiently quantify the ethane and methane in the exoplanet's atmosphere.