  We find that the conjectured heterotic SO(32) five-brane sigma model develops
necessarily k-anomalies, and we investigate their form. We show that these
anomalies can be absorbed by modifications of the superspace constraints, that
satisfy automatically the modified Bianchi-identity $dH_7=X_8$ of N=1, D=10
supergravity. The k-anomalies induce in particular a quantum deformation of the
torsion constraint $T_{\alpha\beta}^a=2\gamma_{\alpha\beta}^a$.
