To account for the observed multiplet structure and the mass relations among the known elementary particles, a coupling of internal and space-time properties is considered. Earlier attempts in this direction have failed. The problem is re-examined from a more general point of view, and it is found that under these more relaxed conditions a coupling is possible and nontrivial mass relations may be obtained. The coupling can be described as a "minimal internal coupling," which essentially consists of a replacement of the original generators of the inhomogeneous Lorentz group. The characteristic features of the mass formula are exhibited in a simple model. A number of questions related to the interpretation of such quantities as mass and energy are raised.