  We study the concept of liaison addition for codimension two subschemes of an
arithmetically Gorenstein projective scheme. We show how it relates to liaison
and biliaison classes of subschemes and use it to investigate the structure of
Gorenstein liaison equivalence classes, extending the known theory for complete
intersection liaison of codimension two subschemes. In particular, we show that
on the non-singular quadric threefold in projective 4-space, every non-licci
ACM curve can be obtained from a single line by successive liaison additions
with lines and CI-biliaisons.
