The article presents the results of molecular-dynamics calculations of the isochoric heat capacity, c(nu), and the (p, p, T) - properties of the Lennard-Jones fluid in the region of liquid-gas phase transition in stable and metastable states. The system under investigation contains 2048 particles, the cut-off radius of the potential is chosen equal to 6.78 sigma. The results of computations of the (p, p, T) - properties have been used to approximate the location of the spinodal. Values of c(nu) have been determined along the gas and the liquid branches of the spinodal. A thermodynamic relation that determines the value of c(nu) on the spinodal in terms of derivatives with respect to temperature of the entropy, pressure and specific volume along the spinodal has been obtained. It is shown that molecular-dynamics data are in agreement with the results of the thermodynamic analysis. 2007 Elsevier B.V. All rights reserved.