  We address a general system of nonlinear Dirac equations in (1+1) dimensions
and prove nonexistence of classical self-similar blowup solutions in the space
of bounded functions. While this argument does not exclude the possibility of
finite-time blowup, it still suggests that smooth solutions to the nonlinear
Dirac equations in (1+1) dimensions do not develop self-similar singularities
in a finite time. In the particular case of the cubic Dirac equations, we
characterize (unbounded) self-similar solutions in the closed analytical form.
