  Spaces equipped with congruences of null strings are considered. A special
attention is paid to the spaces which belong to the two-sided Walker class and
para-K\"ahler class. Properties of an intersection of self-dual and
anti-self-dual congruences of null strings are used as an additional criterion
for a classification of such spaces. Finally, a few examples of para-K\"ahler
and para-K\"ahler-Einstein spaces are presented.
