  The {\it {gauge - fixing} } and {\it gaugeless } methods for reducing the
phase space in the generalized Hamiltonian dynamics are compared with the aim
to define the class of admissible gauges . In the gaugeless approach, the
reduced phase space of a Hamiltonian system with the first class constraints is
constructed locally, without any gauge fixing, using the following procedure:
abelianization of constraints with the subsequent canonical transformation so
that some of the new momenta are equal to the new abelian constraints. As a
result the corresponding conjugate coordinates are ignorable ( nonphysical )
one while the remaining canonical pairs corresponds to the true dynamical
variables. This representation for the phase space prompts us the definition of
subclass of admissible gauges -- canonical gauges as functions depending only
on the ignorable coordinates. A practical method to recognize the canonical
gauge is proposed .
