The aim of this paper is to answer the following question. For a spatial groupoidG, i.e. for a groupoid in the category Sp of spaces (in the sense of [20]) in a topos, and continuous maps, the toposBG, of étaleG-spaces, is called ‘the classifying topos of G’ by Moerdijk[22]. This terminology is suggested by the case ofGa discrete group (in Sets), as thenBG, the topos ofG-sets, classifies principalG-bundles. This means that, for each topological spaceX, there is a bijection between isomorphism classes of principalG-bundles overXand isomorphism classes of geometric morphisms from Sh(X) toBG. The question is: what doesBGclassify, in terms ofG, in the general case of a spatial groupoidGin a topos?