The mean ionic activity coefficients of dilute electrolyte solutions show large anomalies near the critical point of water. Activity coefficients of aqueous NaCl solutions were calculated with an electrolyte equation of state at several different near-critical temperatures and densities. At the critical point, the activity coefficients are proportional to x(1/3), where x is the mole fraction of solute, which is consistent with a classical expansion of the Helmholtz free energy near the critical point. At all points, except exactly at the critical point, the Debye-Huckel limiting law is valid in a range that diminishes as the critical point is approached; also vestiges of the x(1/3) limiting law appear at higher concentrations. For ions, large (50%) anomalies in the activity coefficients of 0.01 m NaCl solutions are seen at up to 100 degreesC above the critical temperature and 0.2 g/cm(3) above the critical density. In the present model, these anomalies are large for ions because of significant electrostriction that increases the dielectric constant of water. The electrical conductance measurements on NaCl near the critical point of water indicate that the present model may overestimate the anomalous effect.