  In the present work, we study Yetter-Drinfeld algebras over a pairing of
multiplier Hopf algebras. Our main motivation is the construction of a
self-dual theory of (C*-)algebraic quantum transformation groupoids. Instead of
the standard characterization of Yetter-Drinfeld algebras given in the case of
Hopf algebras, we develop an equivalent "only coaction" characterization in the
framework of multiplier Hopf algebras. Finally, as a special case, we focus on
Yetter-Drinfeld structures over Van Daele's algebraic quantum groups.
