  In this study, using the Brown-Spencer theorem and in the ligth of the works
of Norrie, in the category of internal categories within groups, also called
group-groupoids, we interpret the notion of actor of a crossed module over
groups. Further, we construct the action of a group-groupoid on a
group-groupoid. Moreover, we give the explicit construction of semi-direct
product of two group-groupoids and of holomorph of group-groupoids.
