  Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero
cosmological constant $\Lambda$ equipped with a nonnul Killing vector are
considered. It is shown, that any conformally nonflat metric of such spaces can
be always brought to a special form and the Einstein field equations can be
reduced to the Boyer-Finley-Pleba\'nski equation (Toda field equation). Some
alternative form of the metric are discussed. All possible real slices
(neutral, Euclidean and Lorentzian) of ASD complex spaces admitting a nonnull
Killing vector are found.
