  We consider the contributions to the neutrinoless double beta decays in a
$SU(3)_L\otimes U(1)_N$ electroweak model. We show that for a range of the
parameters in the model there are diagrams involving vector-vector-scalar and
trilinear scalar couplings which can be potentially as contributing as the
light massive Majorana neutrino exchange one. We use these contributions to
obtain constraints upon some mass scales of the model, like the masses of the
new charged vector and scalar bosons. We also consider briefly the decay in
which besides the two electrons a Majoron-like boson is emitted.
