The Krichevskii parameter determines the sign and magnitude of the near-critical divergence of the partial molar thermodynamic properties of infinitely dilute solutions. Estimation of the values of the Krichevskii parameter, A(Kr), would be helpful in improving the quality of predictions of the infinite dilution partial molar properties of aqueous nonelectrolytes at near-critical and supercritical conditions. In this paper, we discuss the methods to obtain values of A(Kr) from various types of experimental information on the thermodynamic properties of binary systems, and use these methods to evaluate the Krichevskii parameter for more than 30 aqueous nonelectrolytes. The possibility of calculating the values of the Krichevskii parameter for solutes at infinite dilution in water from the van der Waals and Peng-Robinson equations of state was also checked. It is shown that the classical cubic equations of state may be used to predict the values of A(Kr) for small nonpolar solutes in water, but grossly overestimate A(Kr) for larger compounds. As an alternative, we propose an empirical correlation between the Krichevskii parameter and the Gibbs energy of hydration at 298.15 K and 0.1 MPa for the corresponding compound. This correlation seems to hold for solutes with values of the Krichevskii parameter ranging from - 200 to + 200 MPa, and values of the Gibbs energy of hydration extending over 100 kJ mol(-1), and appears to be useful for estimating values of the Krichevskii parameter for many solutes of different sizes and polarities: from inert gases to aqueous silica. Predictions, related to the sign of the Krichevskii parameter for a number of aqueous inorganic and organic nonelectrolytes, are made, which can be verified experimentally. (C) 2001 Elsevier Science B.V. All rights reserved.