  Starting from the standard supertwistor realizations for conformally
compactified N-extended Minkowski superspaces in three and four space-time
dimensions, we elaborate on alternative realizations in terms of graded
two-forms on the dual supertwistor spaces. The construction is further
generalized to the cases of 4D N=2 and 3D N-extended harmonic/projective
superspaces. We present a superconformal Fourier expansion of tensor
superfields on the 4D N=2 harmonic/projective superspace.
