A first-principles interaction potential proposed by Pacheco and Ramalho (PRP) and the effective potential of Girifalco (GP) have been used to model the whole phase diagram Of C-60 by Gibbs ensemble and Gibbs-Duhem integration Monte Carlo methods. The triple-point properties were determined by a direct method recently proposed by us (Comput. Phys. Commun. 2001, 141, 403). It is based on the behavior of the Gibbs ensemble vapor-liquid simulations at the low-temperature limit, and it does not involve free-energy calculations. A stable liquid phase for temperatures between 1570 +/- 20 K and 2006 +/- 27 K is predicted with the PRP model and for temperatures between 1529 +/- 36 K and 1951 +/- 28 K with the GP model. According to these results, the liquid phase for C-60 extends over similar to450 K, a temperature range considerably wider than the ones reported by other authors on the basis of free-energy calculations and density functional approaches. Nonetheless, the present results are in good agreement with the theoretical predictions from the hypernetted mean spherical approximation, the modified hypernetted chain theory, and a correlative self-consistent field method as well as with some molecular dynamics simulations. The reported free-energy data for the fluid-solid region are reproduced here, strictly by computer simulation. According to them, the liquid phase Of C-60 extends over similar to100 K. A discussion on the apparent conflicting triple-point data is presented. The calculated enthalpies of sublimation at 700 K (163 +/- 9 M mol(-1) for PRP and 170 +/-12 kJ mol(-1) for GP) are in good agreement with the available experimental results. The estimated standard enthalpies are also within the recommended values, and the third-law enthalpies are in excellent agreement with experimental and theoretical data. This suggests that at least the simulated triple-point properties, in the low-temperature limit, should approach that of real C-60. The radial distribution functions and the self-diffusion coefficients, in the liquid pockets predicted for the two models, are also consistent with a normal liquid state, and no sign of liquid supercooling was observed. On the whole, the differences between the present interaction potentials do not induce significant qualitative changes in the phase behavior of the two models. However, the differences are clearly reflected in the location of the coexistence lines and the critical and triple-point properties as well as in the enthalpies of sublimation. Finally, as a further test of the reliability of our method for the determination of triple-point properties, we also report preliminary results for the triple-point temperature and the standard enthalpy of sublimation Of C-70. They are in excellent agreement with theoretical and experimental data.