The deoxidation, desulphuration and deoxysulphuration constants and the standard Gibbs energies (in joules per mole) of formation of the following rare earth compounds as the equilibrium phases in nickel-base solutions have been determined: Ce2O3, lg K = -(6.0729 x 10(4)/T) + 16.50, DELTAG(o) = -1.162460 x 10(6) + 315.84T; Ce2O2S, lg K = -(5.1450 x 10(4)/T) + 12.46, DELTAG(o) = -9.84850 x 10(5) + 238.50T; Ce2S3, lg K = -(7.2232 x 10(4)/T) + 27.98, DELTAG(o) = -1.382600 x 10(6) + 535.55T; Y2O3, lg K = -(4.2572 x 10(4)/T) + 7.74, DELTAG(o) = -8.14920 x 10(5) + 148.16T; Y2O2 S, lg K = -(3.3146 x 10(4)/T) + 3.85, DELTAG(o) = -6.34460 x 10(5) + 73.72T; Y2S3, lg K = -(1.22487 x 10(5)/T) + 55.78, DELTAG(o) = -2.344630 x 10(6) + 1067.76T. The interaction coefficients of cerium and yttrium with oxygen were determined as e(O)Ce = -(3.33451 x 10(5)/T) + 149.7 and e(O)Y = -1.63437 x 10(5)/T) + 71.8. The phase equilibria of Ni-Ce-S-O and Ni-Y-S-O solutions at 1600-degrees-C provide the basis for predicting the sequence and type of cerium and yttrium equilibrium phases formed in nickel-based solutions. The formulae determining the morphology of inclusions formed in liquid nickel by cerium or yttrium addition are also given.