  We introduce new Lorentz-symmetry violating kinematics for a four-fermion
interaction model, where dynamical mass generation is allowed, irrespectively
of the strength of the coupling. In addition, these kinematics lead to a
quasi-relativistic dispersion relation, in the sense that it is relativistic in
both the infrared and the ultraviolet, but not in an intermediate regime,
characterized by the mass $M$. For two fermions, we show that a flavour-mixing
mass matrix is generated dynamically, and the Lorentz symmetric limit
$M\to\infty$ leads to two free relativistic fermions, with flavour
oscillations. This model, valid for either Dirac or Majorana fermions, can
describe any set of phenomenological values for the eigen masses and the mixing
angle.
