  For N-extended superconformal field theories in three spacetime dimensions
(3D), with N=1,2,3, we compute the two- and three-point correlation functions
of the supercurrent and the flavour current multiplets. We demonstrate that
supersymmetry imposes additional restrictions on the correlators of conserved
currents as compared with the non-supersymmetric case studied by Osborn and
Petkou in hep-th/9307010. It is shown that the three-point function of the
supercurrent is determined by a single functional form consistent with the
conservation equation and all the symmetry properties. Similarly, the
three-point function of the flavour current multiplets is also determined by a
single functional form in the N=1 and N=3 cases. The specific feature of the
N=2 case is that two independent structures are allowed for the three-point
function of flavour current multiplets, but only one of them contributes to the
three-point function of the conserved currents contained in these multiplets.
Since the supergravity and super-Yang-Mills Ward identities are expected to
relate the coefficients of the two- and three-point functions under
consideration, the results obtained for 3D superconformal field theory are
analogous to those in 2D conformal field theory.
  In addition, we present a new supertwistor construction for compactified
Minkowski superspace. It is suitable for developing superconformal field theory
on 3D spacetimes other than Minkowski space, such as S^1 x S^2 and its
universal covering space R x S^2.
