Two-sided conformally recurrent 4-dimensional self-dual spaces are considered. It is shown that such equipped with nonexpanding congruences of null strings. The general structure weak hyperheavenly given. Finally, the metrics Petrov-Penrose type $[D] x [-]$ presented.

The class of Petrov type I curvature tensors is further divided into those for which the span set distinct principal null directions has dimension four (maximally spanning I) or three (nonmaximally I). Explicit examples are provided both vacuum and nonvacuum spacetimes.