The (Na + K + S) system is of primary importance for the combustion of black liquor in the kraft recovery boilers in pulp and paper mills. A thermodynamic evaluation and optimization for the (Na + K + S) system has been made. All available data for the system have been critically evaluated to obtain optimized parameters of thermodynamic models for all phases. The liquid model is the quasichemical model in the quadruplet approximation, which evaluates 1st- and 2nd-nearest-neighbour short-range-order. In this model, cations (Na+ and K+) are assumed to mix on a cationic sublattice, while anions (S2-, S-2(2-), S-3(2-), S-4(2-), S-5(2-), S-6(2-), S-7(2-), S-8(2-), Va(-)) are assumed to mix on an anionic sublattice. The thermodynamic data of the liquid polysulphide components M2S1+n (M = Na, K and n = 1-7) are fitted to Delta G = A(n) + B(n) . T for the reaction M2S(1) + nS(1) = M2Sn+1 (1). The solid phases are the alkali alloys, alkali sulphides, several different alkali polysulphides and sulphur. The solid solutions (Na, K), (Na, K)(2)S and (Na, K)(2)S-2 are modelled using the compound energy formalism. The models can be used to predict the thermodynamic properties and phase equilibria in the multicomponent heterogeneous system. The experimental data are reproduced within experimental error limits for equilibria between solid, liquid and gas. The ternary phase diagram of the system (Na2S + K2S + S) has been predicted as no experimental determinations of the phase diagram have been made previously. (C) 2005 Elsevier Ltd. All rights reserved.