Direct molecular-simulation results of the thermodynamic Gruneisen parameter, gamma(G), and the density scaling exponent, gamma, are reported for the Lennard-Jones and the Gaussian core model potential in extended fluid-phase regions, and are compared with results calculated from equations of state. The direct molecular simulation method is based on the calculation of so-called phase-space functions and allows, in principle, the investigation of any thermodynamic property without any restrictive approximation. The Gruneisen parameter and the density scaling exponent are key quantities in the theory of strongly correlating liquids. Therefore, we paid special attention on the relationship between gamma(G) and gamma for the Lennard-Jones system as a strongly correlating fluid. Because the Griineisen parameter can be related to experimentally accessible thermodynamic properties, we analysed in detail the decomposition of gamma(G) into the thermal expansion coefficient, the isothermal compressibility, the isochoric heat capacity, and the thermal pressure coefficient. Moreover, we show that a predicted effective density scaling exponent of gamma approximate to 6 for the Lennard-Jones fluid can be found close to the triple point of the system. The investigation of gamma(G) for the Gaussian core model, which is not a strongly correlating fluid, revealed anomalous behaviour at higher densities with negative values of gamma(G). (C) 2014 Elsevier B.V. All rights reserved.