  A phenomenon of classical quantization is discussed. This is revealed in the
class of pseudoclassical gauge systems with nonlinear nilpotent constraints
containing some free parameters. Variation of parameters does not change local
(gauge) and discrete symmetries of the corresponding systems, but there are
some special discrete values of them which give rise to the maximal global
symmetries at the classical level. Exactly the same values of the parameters
are separated at the quantum level, where, in particular, they are singled out
by the requirement of conservation of the discrete symmetries. The phenomenon
is observed for the familiar pseudoclassical model of 3D P,T-invariant massive
fermion system and for a new pseudoclassical model of 3D P,T-invariant system
of topologically massive U(1) gauge fields.
