Among other applications of the S U ( 3 ) F symmetry, the most interesting ones are those related to its gauge sector. Generally, the family scale M F may be located in the range from 10 5 GeV up to the grand unification scale M G U T and even higher. For the relatively low family scale M F , the S U ( 3 ) F gauge bosons will also enter into play so that there may become important many flavor-changing rare processes including some of their astrophysical consequences. In contrast to the vectorlike family symmetries the chiral S U ( 3 ) F is not generically free from gauge anomalies. They, however, can be readily cancelled by introduction of the appropriate set of the pure horizontal fermion multiplets. Being sterile with respect to all the other Standard Model interactions, they may treated as one of possible candidates for a dark matter in the Universe.