  Two mathematical models based on Pauli transformations including U(1) chiral
group and Pauli SU(2) group, that mixes particle and antiparticle states, are
developed for description of Majorana properties of neutral particles. The
first one describes a system, incorporating left- and right-handed fermions of
the same flavor, and it is a generalization of the Majorana model of his
pioneer article of 1937 year. The second describes a two-flavor neutrino system
with quantum numbers of Zel'dovich-Konopinsky-Mahmoud (ZKM) type. For massless
fermions the Pauli symmetry is exact and leads to the coserved generalized
lepton charge. It is a Pauli isospace vector, whose different directions are
coordinated with Dirac or generalized Majorana properties. In nonzero-mass case
the models describe the combined Dirac-Majorana properties of neutral
particles, which are characterized either by the generalized lepton charges of
ZKM-type or by the eigenvalues of the operator that is the product of the
charge operator and chirality. The latter is connected with operator of the
structure of Lagrangian mass term or with the generalized flavor number of the
second model. The choice of the basic operator depends on the inversion classes
(A-B or C-C - types) of the particles with respect to the space inversion. The
modified second model can be used for description of neutrino oscillation in
the simplest two-flavor case.
