  The constrained Hamiltonian systems admitting no gauge conditions are
considered. The methods to deal with such systems are discussed and developed.
As a concrete application, the relationship between the Dirac and reduced phase
space quantizations is investigated for spin models belonging to the class of
systems under consideration. It is traced out that the two quantization methods
may give similar, or essentially different physical results, and, moreover, a
class of constrained systems, which can be quantized only by the Dirac method,
is discussed. A possible interpretation of the gauge degrees of freedom is
given.
