Exploration of the mutual scattering of photons in vacuum is considered as a fundamental test of the quantum electrodynamics theory. In this connection, we propose a "double" free-electron laser oscillator as a possible device for head-on photon-photon collisions. The device is conceived to comprise two undulator sections within the same cavity, where then two laser beams are produced by two counterpropagating electron beams. The latter are in turn exploited to produce gamma photons by backward Compton scattering of the intracavity FEL radiation itself. A preliminary analysis of the collision rate of the backscattered photons is presented specifically at the maximum of the relevant cross section. © 2013 Elsevier B.V.