Representations of four-dimensional superconformal groups on harmonic super
fields are discussed. It is shown how various short representations can be
obtained by parabolic induction. It is also shown that such short multiplet
s may admit several descriptions as superfields on different superspaces. I
n particular, this is the case for on-shell massless superfields. This allo
ws a description of short representations as explicit products of fundament
al fields. Superconformal transformations of analytic fields in real harmon
ic superspaces are given explicitly.