  The old issue of why there are more than one family of quarks and leptons is
reinvestigated with an eye towards the use of anomaly as a tool for
constraining the number of families. It is found that, by assuming the
existence of right-handed neutrinos (which would imply that neutrinos will have
a mass) and a new chiral SU(2) gauge theory, strong constraints on the number
of families can be obtained. In addition, a model, based on that extra SU(2),
is constructed where it is natural to have one "very heavy" fourth neutrino and
three almost degenerate light neutrinos whose masses are all of the Dirac type.
