Although the 1-component O(3,1)O of the full Lorentz groupO(3,1) has only one universal covering group, it is shown thatO(3, 1) has eight nonisomorphic simply connected covering groups. These are determined explicitly and their representation theory is given. There are arguments showing that the true symmetry group of relativistic particles is notO(3,1) but one or several of the 8 covering groups. This leads to a classification of particles into eight (possibly empty) classes. Particles belonging to different classes cannot make an interference. Two classes do not possess true finite dimensional irreducible representations. The existence of a spin structure in the sense of one of these covering groups will probably lead to limitations of the topology of space-time not yet investigated.