Two stable solid phases with composition in the range from (45 to 48) moles per cent of S exist for (nickel+sulfur) : Ni9S8 which disproportionates to Ni1-deltaS and Ni7+/-deltaS6 above T=(709+/-5) K, and Ni7+/-deltaS6. The latter non-stoichiometric phase forms eutectoidally from Ni9S8 and Ni3S2 at T=(675+/-3) K. It is stable in a rather narrow temperature interval and disproportionates to Ni1-deltaS and Ni3+/-deltaS2 at T=(850+/-2) K. The phases are characterized structurally, and a revised phase diagram is presented. The heat capacity of a sample with composition Ni7S6 was determined over the temperature range T=5 K to 970 K by adiabatic calorimetry. Effects from metastable modifications of the high-temperature phase were observed during thermal analysis, X-ray diffraction, and calorimetry on incompletely equilibrated samples. Thermodynamic-function values for Ni7S6 and Ni9S8 are presented.