The isochoric heat capacity of two (0.5004 and 0.5014 mole fraction of methanol) H20+CH30H mixtures has been measured in a range of temperatures from 371 to 579 K and densities between 214 and 394 kg m(-3). Measurements were made with a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. The measurements were performed in the one- and two-phase regions including the coexistence curve, and in the near-critical and supercritical regions. Temperatures at the phase transition curve T-S(rho) for each of the measured densities and the critical parameters (T-C and rho(C)) for the 0.4996H(2)O + 0.5004CH(3)OH mixture were obtained using the method of quasi-static thermograms. The uncertainty of the heat-capacity measurements is estimated to be 2%. Uncertainties of the density, temperature and concentration measurements are estimated to be 0.15%, 15 mK and 5 x 10(-5) mole fraction, respectively. The derived values of the critical parameters, together with published data, were used to calculate the value of the Krichevskii parameter. The near-critical isochoric heat capacity behavior for the 0.4996H(2)O+0.5004CH(3)OH mixture was studied using the principle of isomorphism of the critical phenomena in binary mixtures. (c) 2006 Elsevier B.V. All rights reserved.