  We analyse the normal quotient structure of several infinite families of
finite connected edge-transitive, four-valent oriented graphs. These families
were singled out by Marusic and others to illustrate various different internal
structures for these graphs in terms of their alternating cycles (cycles in
which consecutive edges have opposite orientations). Studying the normal
quotients gives fresh insights into these oriented graphs: in particular we
discovered some unexpected `cross-overs' between these graph families when we
formed normal quotients. We determine which of these oriented graphs are
`basic', in the sense that their only proper normal quotients are degenerate.
Moreover, we show that the three types of edge-orientations studied are the
only orientations, of the underlying undirected graphs in these families, which
are invariant under a group action which is both vertex-transitive and
edge-transitive.
