  One of pressing problems in mathematical physics is to find a generalized
Poincar\'e symmetry that could be applied to nonflat space-times. As a step in
this direction we define the semidirect product of groupoids $\Gamma_0 \rtimes
\Gamma_1$ and investigate its properties. We also define the crossed product of
a bundle of algebras with the groupoid $\Gamma_1$ and prove that it is
isomorphic to the convolutive algebra of the groupoid $\Gamma_0 \rtimes
\Gamma_1$. We show that families of unitary representations of semidirect
product groupoids in a bundle of Hilbert spaces are random operators. An
important example is the Poincar\'e groupoid defined as the semidirect product
of the subgroupoid of generalized Lorentz transformations and the subgroupoid
of generalized translations.
