  We classify non-trivial (non-central) extensions of the group $Diff^+(S^1)$
of all diffeomorphisms of the circle preserving its orientation and of the Lie
algebra $Vect (S^1)$ of vector fields on $S^1$, by the modules of
tensor-densities on $S^1$. The result is: 4 non-trivial extensions of
$Diff^+(S^1)$ and 7 non-trivial extensions of $Vect (S^1)$. Analogous results
hold for the Virasoro group and the Virasoro algebra. We also classify central
extensions of constructed Lie algebras. CPT-94/P.3024
