Heat capacities of dilute aqueous solutions of methane, carbon dioxide, hydrogen sulfide and ammonia were measured at temperatures ranging from 300 K to 705 K and at pressure 28 MPa. The thermodynamic behaviour of aqueous non-electrolytes in the supercritical region is discussed. The results show the expected very large maximum and minimum near the critical density of water. Methods of correlating and predicting values of V-m,V-2 and C-p,C-m,C-2 are explored.