The specific heats at constant volume, Cv, of pure water have been measured at 12 isochores ranging from 255.76 kg.m -3 to 426.99 kg.m -3, at temperatures between 643.61 K and 660.87 K. The measurements were performed using a high-temperature constant volume adiabatic calorimeter. The uncertainty of most of the measurements is estimated to be less than 1.5 percent. For the 6 isochores (p>pc) metastable states were observed when the calorimeter was cooled through the coexistence curve. For these isochores we have also measurements of the Cv in the metastable states. The results of heat-capacity measurements were used to determine the pseudospinodal curve.