  We study two aspects of fermionic T-duality: the duality in purely fermionic
sigma models exploring the possible obstructions and the extension of the
T-duality beyond classical approximation. We consider fermionic sigma models as
coset models of supergroups divided by their maximally bosonic subgroup
OSp(m|n)/SO(m) x Sp(n). Using the non-abelian T-duality and a non-conventional
gauge fixing we derive their fermionic T-duals. In the second part of the
paper, we prove the conformal invariance of these models at one and two loops
using the Background Field Method and we check the Ward Identities.
