Gauge theories with gauge potential that is an abelian 2-form or 3-form are relatively well understood and are relevant in supergravity and in string theory. We study the nonabelian version of these gauge theories, in particular their underlying geometry. We see that a relaxed version of the notion of connection one form on a principal bundle is necessary in the context of nonabelian gerbes. We then give evidence that such nonabelian gerbes are relevant for the description of a stack of M5-branes in M-theory.