We discuss the uv finiteness of the two-dimensional BF model coupled to top
ological matter quantized in the axial gauge. This noncovariant gauge fixin
g avoids the ir problem in the two-dimensional space-time. The BF model tog
ether with the matter coupling is obtained by dimensional reduction of the
ordinary three-dimensional BF model. This procedure furnishes the usual lin
ear vector supersymmetry and an additional scalar supersymmetry. The whole
symmetry content of the model allows one to apply the standard algebraic re
normalization procedure which we use to prove that this model is uv finite
and anomaly free to all orders of perturbation theory.