The effect of molecular associations on the phase coexistence properties of fluids with one or two directional, attractive centres is investigated. The individual molecules are represented by hard-sphere repulsive cores with off-centre, square-well attractive sites. Such a system’s thermodynamic properties can be calculated by using expressions based on a theory recently proposed by Wertheim. Isothermal-isobaric Monte Carlo simulations of hard-sphere fluids with one or two attractive sites are shown to be in good agreement with the results of the theory. In order to study the system’s phase equilibria using the theory, a simple van der Waals mean-field term is added to account for the dispersion forces. The critical points and phase equilibria of the associating fluids are determined for various values of the strength and range of the attractive site. Furthermore, results are presented for the degree of association in the gas and liquid phases along the vapour pressure curve. The theory can treat fluids with strong hydrogen-bonding associations such as those found in the carboxylic acids, the aliphatic alcohols, hydrogen fluoride, water etc.