  In this work we study examples of hierarchical neutrino mass matrices
inspired by family symmetries, compatible with experiments on neutrino
oscillations, and for which there is a connection among the low energy CP
violation phase associated to neutrino oscillations, the phases appearing in
the amplitude of neutrinoless double beta decay, and the phases relevant for
leptogenesis. In particular, we determine the predictions from a texture based
on an underlying SU(3) family symmetry together with a GUT symmetry, and a
strong hierarchy for the masses of the heavy right handed Majorana masses. We
also give some examples of inverted hierarchies of neutrino masses, which may
be motivated in the context of U(1) family symmetries.
