  We discuss symmetries and scenarios leading to quasi-degenerate neutrinos in
type-I seesaw models. The existence of degeneracy in the present approach is
not linked to any specific structure for the Dirac neutrino Yukawa coupling
matrix $y_D$ and holds in general. Basic input is the application of the
minimal flavour violation principle to the leptonic sector. Generalizing this
principle, we assume that the structure of the right handed neutrino mass
matrix is determined by $y_D$ and the charged lepton Yukawa coupling matrix
$y_l$ in an effective theory invariant under specific groups ${\cal G}_F$
contained in the full symmetry group of the kinetic energy terms. ${\cal G}_F$
invariance also leads to specific structure for the departure from degeneracy.
The neutrino mass matrix (with degenerate mass $m_0$) resulting after seesaw
mechanism has a simple form ${\cal M}_\nu\approx m_0(I-p y_ly_l^T)$ in one
particular scenario based on supersymmetry. This form is shown to lead to
correct description of neutrino masses and mixing angles. The thermal
leptogenesis after inclusion of flavour effects can account for the observed
baryon asymmetry of the universe within the present scenario. Rates for lepton
flavour violating processes can occur at observable levels in the
supersymmetric version of the scenario.
