M. Dimassi and J.-C. guillot The quantum electrodynamics of relativistic bound states with cutoffs.I. (349K, Postscript) ABSTRACT. In this note we consider an Hamiltonian with cutoffs describing the interaction of relativistic electrons and positrons in a Coulomb potential with transversal photons in Coulomb gauge. We prove that the Hamiltonian is self-adjoint in the Fock space and has a ground state for a sufficiently small coupling constant.