Results of a systematic investigation of the vapour-liquid equilibria of 38 individual two-centre Lennard-Jones plus axial pointdipole model fluids (2CLJD) are reported over a range of reduced dipolar momentum 0 less than or equal to mu*(2) less than or equal to 20 and of reduced elongation 0 less than or equal to L* less than or equal to 1.0. Temperatures investigated are from about 55 to 95% of the critical temperature of each fluid. The NpT + test particle method is used for the generation of vapour pressures, saturated densities, and saturated enthalpies. For the lowest temperatures, these data are calculated with highly accurate chemical potentials obtained from the gradual insertion method. Critical temperatures T-c* and densities rho(c)* are obtained from Guggenheim's equations. Empirical correlations for critical data T-c* and rho(c)* as well as for saturated densities rho'* and rho"*, and vapour pressures p(sigma)* are developed as global functions of the model parameters. They describe the simulation data generally within their statistical uncertainties. Critical pressures and acentric factors of the 2CLJD fluid can be calculated from these correlations. The present results are a sound basis for adjustments of the model parameters mu*(2), L*, sigma and epsilon to experimental VLE data of real fluids. (C) 2003 Elsevier Science B.V. All rights reserved.