We shall use the language of Lie groupoids and Morita equivalence to introduce gerbes, and connections on them. The advantage of this presentation is that it makes it possible to use ordinary differential geometry, without going to "higher" objects - the default being the need to check the invariance of all constructions under Morita equivalence. I shall try to relate this construction with previous ones, especially the constructions of Breen and Messing.

We introduce nonabelian bundle 2-gerbes related to Lie 2-crossed modules and discuss their properties. Such bundle 2-gerbes are defined in terms of bundle 1-gerbes, which play a role similar to that of transition functions in the theory of principal bundles.