The possiblities of merging QED with the standard many-body perturbation theory (MBPT) for atomic systems in a rigorous and systematic way are analysed. Time-dependent MBPT, based on the time-evolution operator, a technique well developed particularly in nuclear theory, is used and somewhat reformulated to be consistent with the covariant QED formalism. An effective QED Hamiltonian, free from singularities, is constructed. The procedure can be applied to degenerate and quasi-degenerate systems (extended model space), which is not possible with the standard QED technique based upon theS-matrix formulation. To include in the model space closely lying energy levels, such as fine-structure levels, can have a dramatic effect on the convergence rate. The electron-electron interaction is investigated in detail, and it is shown that it can be separated into irreducible multi-photon interactions, which in principle can be iterated as in standard MBPT. Singularities do not appear, and a simple procedure for evaluating residual finite contributions is described. Comparison is made with the closely related Green's function technique. The procedure is presently being tested on the fine-structure levels of He-like ions.