  We study the Morita equivalence for fermion theories on noncommutative
two-tori. For rational values of the $\theta$ parameter (in appropriate units)
we show the equivalence between an abelian noncommutative fermion theory and a
nonabelian theory of twisted fermions on ordinary space. We study the chiral
anomaly and compute the determinant of the Dirac operator in the dual theories
showing that the Morita equivalence also holds at this level.
