Abstract: 
\def\cf{{\cal F}}For every 
Lie groupoid $\Phi$ with $m$-dimensional base $M$
and every fiber product preserving bundle functor $F$ on the
category of fibered manifolds with $m$-dimen\-sion\-al
bases and fiber preserving maps with local diffeomorphisms
as base maps, we construct a Lie groupoid $\cf \Phi$ over
$M$.
Every action of $\Phi$ on a fibered manifold $Y\to M$ is
extended to an action of $\cf \Phi$ on $FY\to M$.

1. Faculty of Science
   Masaryk University
   Janáèkovo nám. 2a
   602 00 Brno, Czech Republic