The PY-integral equation has been applied for the model system consisting of monatomic molecules A and B obeying the Lennard-Jones potential law so as to establish the molecular basis for interpretation of excess thermodynamic quantities of solutions. The potential parameters used are sigma(AA) = 1.0 and sigma(BB) = 0.9283, as well as epsilon(AA) = 1.0 and epsilon(BB) = 0.8. These parameters are set as sigma(AA)/(sigma(BB))(3) = epsilon(AA)/epsilon(BB). The critical parameters of these fluids are known to be (P-c, T-c) = (0.129, 1.32) for species A and (0.129, 1.06) for species B and calculation has been carried out in the region where pressure and temperature are simultaneously below the critical values, The formalism proposed recently by Ohba and Nomura (J. Phys. Chem., 99, 12355 (1995)) has been adopted and the excess thermodynamic quantities such as excess volume V-E, excess enthalpies H-E, and excess specific heat capacities Cp-E have been evaluated. Pressure dependence was one order of magnitude smaller than the case of temperature dependence and that the change of temperature from 0.95 to 1.0 gives rise to far more remarkable effect on the excess quantities than for the temperature change from T = 0.8 to 0.9. The components contributing to the partial molecular enthalpy and the specific heat capacity have been evaluated.