This letter focuses on the matter of the Hamiltonian description of reducib
le dynamical systems using the BRST technique. We will have in mind importa
nt examples as the Freedman-Townsend one or the bosonic string, both endowe
d with an sp(3) BRST symmetry. For the first time, for such type of theorie
s, a structure of the extended phase space will be proposed, as well as the
forms of the BRST charges and of the extended Hamiltonian.