  For a conformal theory it is natural to seek the conformal moduli space, M_c
to which it belongs, generated by the exactly marginal deformations. By now we
should have the tools to determine M_c in the presence of enough supersymmetry.
Here it is shown that its dimension is determined in terms of a certain index.
Moreover, the D-term of the global group is an obstruction for deformation, in
presence of a certain amount of preserved supersymmetry. As an example we find
that the deformations of the membrane (3d) field theory, under certain
conditions, are in 35/SL(4,C). Other properties including the local geometry of
M_c are discussed.
