  The $w^{\star}$-rigged modules over dual operator algebras were introduced by
Blecher and Kashyap as a generalization of $W^{\star}$-modules. In this paper,
we introduce two new types of Morita equivalence between right
$w^{\star}$-rigged modules over unital dual operator algebras and we examine
whether these notions imply stable isomorphism between the corresponding
modules. Furthermore we investigate them in detail for the class of right
$w^{\star}$-rigged modules over nest algebras, that was characterised by
G.K.Eleftherakis.
