  Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear
(gauge) transformation acting in the corresponding state space. The
construction generalises a construction for nonlinear Schr\"odinger equations.
To relate N^2 with physically motivated principles we assume: locality (i.e. it
contains no explicit derivative and no derivatives of the wave function),
separability (i.e. it acts on product states componentwise) and Poincar\'e
invariance. Furthermore we want that a positional density is invariant under
N^2. Such nonlinear transformations yield NLDE which describe physically
equivalent systems. To get 'new' systems, we extend this NLDE (gauge extension)
and present a family of NLDE which is a slight nonlinear generalisation of the
Dirac equation. We discuss and comment the fact that nonlinear evolutions are
not consistent with the usual framework of quantum theory. To develop a
corresponding extended framework one needs models for nonlinear evolutions
which also indicate possible physical consequences of nonlinearities.
