  We introduce the notion of \textbf{Q}-principal bundle, which is the
appropriate version of principal fibre bundles in the setting of R. Barre's
\textbf{Q}-manifolds. As an application, we prove that every transitive Lie
algebroid arises from the Atiyah sequence of a certain \textbf{Q}-principal
bundle, and we give the interpretation of this result in terms of groupoids.
