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ZnS nanopowders and ZnS/Ag2S heteronanostructures have been synthesized by chemical deposition from aqueous solutions. A change in the ratio between the concentrations of reagents in the reaction mixtures made it possible to obtain ZnS nanopowders with an average particle size of 2 to 10 nm. The size of Ag2S nanoparticles in the prepared heteronanostructures is 9-30 nm, the thickness of ZnS surface layer is 4-5 nm. The diffuse reflection spectra of nanostructured ZnS and ZnS/Ag2S heteronanostructures have been measured. By the analysis of measured spectra, the width of band gap Eg in studied sulfide nanostructures is estimated. The optical band gap Eg of the studied sulfide nanostructures has been estimated. An increase in the Eg values from 3.17 to 3.36 eV is observed with a decrease in the size of ZnS nanoparticles from 10 to 2 nm. An increase in the Ag2S content in ZnS/Ag2S heteronanostructures leads to a decrease in the optical band gap and decreasing the luminescence intensity.