We introduce a natural notion of strong Morita equivalence of twisted
coactions on C-algebras and then show that the corresponding twisted
crossed product C-algebras are strongly Morita equivalent. This is an
analogue of the notion of strong Morita equivalence of Green's twiste
d actions. We also present criteria for strong Morita equivalence of c
rossed products by coactions and produce a family of twisted coactions
on a groupoid C-algebra. (C) 1994 Academic Press. Inc.