The complete proof of a theorem announced in Ref. 1 on the consistent inter
actions for (nonchiral) exterior form gauge fields is given. The theorem ca
n be easily generalized to the analysis of anomalies. Its proof amounts to
computing the local BRST cohomology H-0(s \ d) in the space of local n-form
s depending an the fields, the ghosts, the antifields and their derivatives
.