  We study the two-dimensional supersymmetric Toda theory based on the Lie
superalgebra $B(1,1) \equiv Osp(3|2)$ and construct its quantum W-currents. We
also investigate the fermionic affinization of this model: we show that despite
the non-unitary form of the Lagrangian the $B^{(1)}(1,1)$ theory has a real
particle mass spectrum which is not renormalized at one-loop. We construct the
first higher--spin conserved current, prove its conservation to all-loop order,
compute one-loop corrections to the corresponding charge and check consistency
between charge and mass renormalization.
