[en] In a recent paper we studied the construction of geometries which have different characteristics in the exterior and interior of a hadron, e.g., are conventional in the exterior case, but generalized in the interior one. In this paper we continue this study under the more specific condition that a hadron is a closed non-selfadjoint system, that is, it verifies the general conservation laws of total quantities, but the internal forces are of non-potential type. We begin our study with the indication that non-Desarguesian geometries apply to open non-selfadjoint systems, such as particles under a combination of a constant gravitational field and resistive forces. We then pass to the problem of structure of a hadron by pointing out that the departures from conventional relativity settings in the interior strong problem indicated by recent experiments suggest that the right geometry for a hadron could have a suitable combination of non-Euclidean and non-Desarguesian characters. All possible models of non-Euclidean geometries are exhibited first. We then pass to the identification of as many non-Desarguesian planes as made possible by available axiomatic, algebraic and group theoretical approaches. The construction of a geometry which is non-Euclidean (e.g., Galilean or Minkowskian) in the exterior problem, and non-Desarguesian in the interior case is then discussed. We provide a geometric interpretation of the recent discovery of the violation of the time-reversal symmetry announced at our Conference by Slobodrian and Conzett, as well as the violation of the SU(2)-spin symmetry indicated by Rauch's experiments. In fact, our geometries can recover these symmetries for the trajectory of the center of mass of a hadron, while the symmetries are violated in the interior strong problem