Proper conformal symmetries in self-dual (SD) Einstein spaces are considered.
It is shown, that such symmetries are admitted only by the Einstein spaces of
the type [N]x[N]. Spaces of the type [N]x[-] are considered in details.
Existence of the proper conformal Killing vector implies existence of the
isometric, covariantly constant and null Killing vector. It is shown, that
there are two classes of [N]x[-]-metrics admitting proper conformal symmetry.
They can be distinguished by analysis of the associated anti-self-dual (ASD)
null strings. Both classes are analyzed in details. The problem is reduced to
single linear PDE. Some general and special solutions of this PDE are
presented
