The measurement of extended X-ray absorption fine structure (EXAFS) using energy-selective fluorescence detection in the soft X-ray region has enabled sulfur K-edge EXAFS studies of the amorphous sulfides WS₃, WS₅ and Re₂S₇, to be carried out for the first time. Quantitative information about the local environment of sulfur in these highly structurally disordered sulfides has been obtained and is compared with that obtained by previous EXAFS studies at the metal L_III edges. The average oxidation state of sulfur and hence the metals in these amorphous sulfides is derived from S–S co-ordination numbers. Results from the crystalline model compound [NH₄]₂[W₃(µ₃-S)(µ-S)₃(S₄)₃(NH₃)₃] are also presented to give an indication of the reliability of the results. In all the amorphous compounds studied S–S bonds with bond lengths close to 2.0 Å are found. In WS₃ each sulfur has on average 0.5 sulfur near neighbours and close to 2 tungsten near neighbours at 2.43 Å. In WS₅ each sulfur has on average 1 sulfur near neighbour and ≈1.2 tungsten near neighbours at 2.46 Å, consistent with the material being formulated as W^V(S₂^2–)_2.5. Amorphous Re₂S₇ also contains sulfur with an average sulfur co-ordination number of 1 and the compound is thus formulated as Re^3.5₂(S₂^2–)_3.5. The S–Re bond distance is found to be 2.32 Å. All the S-M distances found are in excellent agreement with those found from previous metal L_III-edge EXAFS studies. Possible structural models for the amorphous materials are discussed.