The invention relates to a one-part dental adhesive composition comprising polymerizable component(s) with an acidic moiety as Component A, photo-initiator(s) as Component B1, transition metal ion component(s) as Component C, solvent(s) other than water as Component D1, a stabilizer as Component E, the stabilizer comprising a free radical moiety or being selected from anaerobic stabilizers, for use in a process of fixing a composite material to the surface of hard dental tissue, the composite material comprising a redox initiator system with an oxidizing agent and a reducing agent.