Grand Unification in Non-associative Geometry

We present the formulation of the SU(5)-GUT and the flipped SU(5) x U(1)-GUT within the framework of non-associative geometry. We find tree-level predictions for the masses of gauge and Higgs bosons. In the SU(5)-model, there is precisely one Higgs field, whose mass is of the order of the mass of the top quark. The remaining 108 Higgs fields are extremely heavy. In the flipped SU(5) x U(1)-model, there occurs an additional massless gauge boson coupling to (barion charge - lepton charge). This gauge boson becomes massive if the right neutrinos are equipped with Majorana masses, which will be done in a forthcoming paper. Without the Majorana mass, there is again the light neutral Higgs field as in the SU(5)-model, but also four coloured Higgs octets whose masses are of the order of the top mass. There are 76 Higgs fields which are extremely heavy