The global phase diagram (i.e., vapor-liquid and fluid-solid equilibrium) of two-center Lennard-Jones (2CLJ) model molecules of bond length L = sigma has been determined by computer simulation. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. In the case of the solid phase, two close-packed solid structures are considered: In the first structure, the molecules are located in layers and all molecular axes point in the same direction; and in the second structure, the atoms form a close-packed arrangement but the molecular axes of the diatomic molecules have random orientations. It is shown that at the vapor-liquid-solid triple-point temperature, the orientationally disordered solid is the stable structure for the solid phase of this model. The vapor-liquid-disordered solid triple-point temperature of the 2CLJ model, with bond length L = sigma, is located at T* = 0.650(4). This is very close to the triple-point temperature of the Lennard-Jones monomer system (T* = 0.687). At very low temperatures, the ordered solid is the stable phase. The vapor-ordered solid-disordered solid triple point is situated at T* = 0.282. The simulation data are compared to Wertheim's first-order thermodynamic perturbation theory (TPT1) for the fluid and solid phases. It is found that Wertheim's TPT1 not only provides an accurate description of the equation of state in both the fluid and solid phases, but also provides accurate values of the free energies. The prediction of Wertheim's TPT1 for the global phase diagram of the 2CLJ model shows excellent agreement with the simulation results, illustrating the possibility of using Wertheim's perturbation theory to determine not only the vapor-liquid equilibria but also the global phase diagram of simple chain model molecules. (C) 2003 American Institute of Physics.