  We have studied the most general neutrino mass matrices in models with SU(2)
and SU(3) horizontal symmetries. Without going into the details of the models
it is possible to write down the effective operators, which predict the
structure of the Majorana neutrino mass matrices. Unlike other extensions of
the standard model, the structure is now independent of the effective Yukawa
couplings and depends entirely on the Higgs which gives mass to the other
fermions. In the case of SU(3) symmetries the lowest dimensional operators are
forbidden requiring a low mass scale for lepton number violation.
