Results of a systematic investigation of the vapour-liquid equilibria (VLE) of 30 individual two-centre Lennard-Jones plus pointquadrupole model fluids (2CLJQ) are reported over a range of reduced quadrupolar momentum 0 less than or equal to Q*(2) less than or equal to 4 and of reduced elongation 0 less than or equal to L* less than or equal to 0.8. Temperatures investigated are from about 55 to about 95% of the critical temperature of each fluid. Uniformly, the NpT + test particle method (NpT + TP method) based on molecular dynamics simulations is used for the generation of vapour pressures, saturated densities, and saturated enthalpies. Critical temperatures T-c* and densities p are obtained from Guggenheim's equations. Empirical correlations for critical data T-c* and rho (c)* as well as for saturated densities rho '*, rho "*, and vapour pressures rho (sigma)* are developed as global functions of the model parameters. In most cases they describe the simulation data within their statistical uncertainties. Critical pressures and acentric factors of the 2CLJQ fluid can be calculated from the correlations. The present simulations are a sound basis for adjustments of the model parameters Q*(2), L*, sigma, and epsilon to experimental VLE data of real fluids. O 2001 Elsevier Science B.V. All rights reserved.