  Hyperplanes and hyperplane complements in the Segre product of partial linear
spaces are investigated . The parallelism of such a complement is characterized
in terms of the point-line incidence. Assumptions, under which the
automorphisms of the complement are the restrictions of the automorphisms of
the ambient space, are given. An affine covering for the Segre product of
Veblenian gamma spaces is established. A general construction that produces
non-degenerate hyperplanes in the Segre product of partial linear spaces
embeddable into projective space is introduced.
