We show that the BF theory in any space-time dimension, when quantized
in a certain linear covariant gauge, possesses a vector supersymmetry
. The generator of the latter together with those of the BRS transform
ations and of the translations form the basis of a superalgebra of the
Wess-Zumino type. We give a general classification of all possible an
omalies and invariant counterterms. Their absence, which amounts to ul
traviolet finiteness, follows from purely algebraic arguments in the l
ower-dimensional cases.