We report the Fickian diffusion coefficients in 20 ternary mixtures formed by 1,2,3,4-tetrahydronaphthalene (THN), isobutylbenzene (IBB) and n-dodecane (nC12) measured by the Taylor dispersion technique at 298.1 K and atmospheric pressure. Four diffusion coefficients of the ternary mixtures were measured along six concentration paths starting on one binary subsystem and moving toward the other one. We found expressions for the diffusion matrix of a ternary mixture approaching to the binary limits. The measured diffusion coefficients were thoroughly verified by comparison with the theoretical asymptotic behavior. The main diffusion coefficients vary smoothly over the entire concentration space and D 11 is always larger than D 22. One of the two cross-diffusion coefficients is of the same order of magnitude as the main ones and, hence, not negligible, whereas the other one is close to zero. The investigated mixtures also comprise compositions that were examined in microgravity experiments in the ESA DCMIX1 project.