The Mean-Field Lattice-Gas model (MFLG) is applied to the description of phase equilibria in systems containing a supercritical fluid and long-chain hydrocarbons. It is shown that two of the four model-parameters for a pure substance depend on the chain length of a hydrocarbon. If the other two parameters are chosen as temperature dependent, they can be kept constant for different hydrocarbons. Both, subcritical VLE-data and supercritical PvT-data of these substances are than described in good quality. The use of an identical set of binary parameters for methane-n-alkanes provides satisfactory results for different binary and ternary mixtures of M-paraffins and supercritical methane. Even for multicomponent n-paraffin systems the dew-point temperature as well as the composition in the coexisting phases can be predicted in good agreement with experimental data. Thus, using the described procedure, the number of parameters needed for phase-equilibrium calculations could be reduced significantly.