Criteria are developed for the occurrence of azeotropes in binary nonelectrolyte systems for both isothermal and isobaric situations in terms of liquid-phase activity coefficients at infinite dilution (gamma(infinity)). In the case of isothermal systems at temperature T, for a positive azeotrope, gamma(lvc)(infinity) >= p(mvc)*/p(lvc)* where lvc refers to the less volatile component, mvc to the more volatile component, and p* to saturation vapour pressure at T, for a negative azeotrope, gamma(mvc)(infinity) <= p(lvc)*/v p(mvc)*. In the case of isobaric systems at pressure P, for a minimum-boiling azeotrope, gamma(lvc)(infinity) (TBmvc) >= P/p(lvc)* (T-Bmvc), where T-B refers to the boiling point at P; for a maximum-boiling azeotrope, gamma(mvc)(infinity) (T-Blvc) <= P/p(mvc)*(T-Blvc). The criteria are also given in terms of the parameters of selected correlations for the excess molar Gibbs function (g(E)). Examples of the use of the criteria are provided. Various methods that generate values of gamma(infinity) can be used in conjunction with the criteria, for example, in screening procedures.