In this paper, we develop a multighost system in gauge field theory, establish the anomalous commutator and anomalous Jacobi “identity” for BRST operators, and point out how to obtain Faddeev's expression of Schwinger term in the commutator of gauge group generators by direct calculation. We show explicitly that Mitra's consistency condition and a new consistency condition are equivalent to the descent equations. We also generalize the descent equations connected with the covariant anomaly up to a 3-cocycle.