A generalized method for thermodynamic consistency to test binary and multicomponent vapour-liquid equilibrium data is reported. The essential step of the method is to solve the coexistence equation (deduced from the Gibbs-Duhem equation). This coexistence equation is an implicit differential equation - an ordinary one in the binary case and a partial one in any other multicomponent case. The unknown function in the differential equation is the molar excess Gibbs energy in all cases.The boundaries of an n-component system consist of the corresponding (n-1) component systems, and the properties of the latter serve also as boundary conditions for the differential equation. Mathematically the following problems arise: Discretization considering the measured points; Multivariable interpolation or fitting in the non-binary cases; Error estimation. Possibilities of the generalization in the n-dimensional space are discussed, and results for the binary and ternary systems are shown.