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Résumé : The phase transitions occurring in the Ising square antiferromagnet with first- (J 1 ) and second- (J 2 ) nearest-neighbour interactions are studied using several mean-field approximations and for a wide range of R=J 2 /J 1 . The largest approximation used corresponds to a nine-point cluster approximation of the cluster variation method. In this case, the transition temperatures as a function of R are found to be in excellent agreement with those obtained by other methods. The mean-field approximations predict a first-order transition in the range 0.5<R<or approximately=1.2, where the critical exponents associated with the paramagnetic to superantiferromagnetic transition have been reported to vary continuously with R. In that range of R, the mean-field approximations also predict a crossover between two distinct instability temperatures, or spinodals, taking place immediately below the first-order transition. Mean-field results are also given for the magnetization m, the specific heat C nu , the magnetic susceptibility X, the staggered susceptibility Xs, and the pair correlation function sigma ij between i and j sites.