  We define multiplicative Poisson-Nijenhuis structures on a Lie groupoid which
extends the notion of symplectic-Nijenhuis groupoid introduced by Sti\'e23non
and Xu. We also introduce a special class of Lie bialgebroid structure on a Lie
algebroid $A$, called P-N Lie bialgebroid, which defines a hierarchy of
compatible Lie bialgebroid structures on $A$. We show that under some
topological assumption on the groupoid, there is a one-to-one correspondence
between multiplicative Poisson-Nijenhuis structures on a Lie groupoid and P-N
Lie bialgebroid structures on the corresponding Lie algebroid.
