The objective of this work is the determination of diagonal and cross-diagonal molecular diffusion coefficients in a ternary mixture, using the ‘Sliding Symmetric Tubes’ (SST) technique. The analyzed mixture consists of two aromatics and one normal alkane (tetrahydronaphthalene–dodecane–isobutylbenzene) with an equal mass fraction for all components (1:1:1) at 25 °C. The analytical solution corresponding to the SST technique has been successfully derived. The different fitting procedures were utilized by two scientific teams to subtract diffusion coefficients from the experimentally measured time-dependent concentration field. None of the attempts provided reliable results for the data from a single experiment. The “simplex”-based methods display reasonable results assuming that cross-diagonal coefficients are close to zero, i.e. quasi-binary and diluted mixtures. The results obtained by “trust region method” are satisfactory if the initial guess is good. To achieve better results, it is necessary to increase the number of experimental data.