Here, we treat the special theory of relativity (SRT). We distinguish the comparison between Galilei geometry and Minkowski geometry, i.e., a comparison of the bare geometries, from comparisons which, in addition, concern physical extensions of these geometries, such as the mechanics of collisions and the mechanics of a mass point in the electromagnetic field. For the comparison of the geometries, we distinguish between the individual limiting case reduction of the Galilei to the Minkowski geometry with variable parameter λ, and asymptotic reductions of one or the other law of the Galilei geometry to a law of the Minkowski geometry with constant \(\lambda = c^{-2}\) . In such a reduction, the geometries as a whole remain untouched. This asymptotic reduction and similar ones are suitable to refute the Kuhn-Feyerabend argument that one can never end up with the Galilean concepts in such an asymptotic ‘derivation’ which starts from the concepts of Minkowski geometry. In relativistic mechanics, too, asymptotic reductions of special mechanical laws can easily be carried out across the gap between the two underlying geometries. However, whether in the mechanics of a mass point Newton’s force equation can generally be reduced to the usual relativistic force equation remains an open question.