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Two SU(8) GUT models (one with fractionally charged color singlet fermions, another with low mass magnetic monopoles) are proposed. Both of them can accomodate three generations of ordinary light fermions.

A two-loop finite SU(6) model is discussed which contains three generations of light quarks and leptons. The masses of quarks and leptons in the model are rather arbitrary except for certain bounds on them. Also the K-M matrix is arbitrary so that the model seems to be a realistic one. The gauge symmetry breaking through SU(6) → SU(3) × SU(2) × U(1) → SU(3) × U(1) em is discussed.

Some SO(18) GUT models are proposed which can accomodate fractionally charged color singlets with ordinary charge ±e 2 and a monopole with ordinary magnetic charge 1 2e . The models are consistent with the Dirac quantisation rule and peculiar photons appear. Future experimental tests of the peculiar photons are discussed. The models can also accomodate four or six generations of ordinary quarks and leptons.

From the requirements of asymptotic freedom, the absence of the triangle anomaly in D = 4 dimensions, the absence of the hexagon anomaly in D = 10 dimensions, and the “generalized Survival Hypothesis”, we find that it is not possible to construct SU(N) GUT models with four generations. But it is possible to build models with three generations, and, there are only two possibilities, namely, SU (8) and SU (9).

The Casalbuoni-Gatto subcomponent model of quarks and leptons in generalized to extend SU(5) of Georgi and Glashow to the high rank group SU( m ) to solve the family problem. It is shown that there is an unique solution with an integral number of families, viz. SU(10) × SU(3) sc .