On gauge fixing and quantization of constrained hamiltonian systems

In constrained hamiltonian systems which posseses first class constraints some subsidiary conditions should be imposed for detecting physical observables. This issue and quantization of the system are clarified. It is argued that the reduced phase space and Dirac method of quantization, generally, differ only in the definition of the Hilbert space one should use. For the dynamical systems possesing second class constraints the definition of physical Hilbert space in the BFV-BRST operator quantization method is different from the usual definition.