  We consider a class of non-unitary Toda theories based on the Lie
superalgebras $A^{(1)}(n,n)$ in two-dimensional Minkowski spacetime, which can
be twisted into a topological sector. In particular we study the simplest
example with $n=1$ and real fields, and show how this theory can be treated as
an integrable perturbation of the $A(1,0)$ superconformal model. We construct
the conserved currents and the vertex operators which are chiral primary fields
in the conformal theory. We then define the chiral ring of the $A^{(1)}(1,1)$
Toda theory and compute topological correlation functions in the twisted
sector. The calculation is performed using a $N=2$ off--shell superspace
approach.
