The hamiltonian BRST-anti-BRST theory is developed in the general case
of arbitrary reducible first class systems. This is done by extending
the methods of homological perturbation theory, originally based on t
he use of a single resolution, to the case of a biresolution. The BRST
and the anti-BRST generators are shown to exist. The respective links
with the ordinary BRST formulation and with the sp(2)-covariant forma
lism are also established.