2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65142In this paper we introduce a generalisation of the notion of holonomy for connections over a bundle map on a principal fibre bundle. We prove that, as in the standard theory on principal connections, the holonomy groups are Lie subgroups of the structure group of the principle fibre bundle and we also derive a straightforward generalisation of the Reduction Theorem.22 pages, no figuresDifferential Geometry53C05; 53C29text