I. INTRODUCTION Consideration of a field theory in an external field background is a longstanding chal- lenging physical problem, that attracts attention owing to many other reasons apart from the fact that the astrophysical reality or laser and accelerator technology do propose elec- tromagnetic fields, so strong as to make the nonlinearity of the theory of electromagnetic interaction actual. The cases of external fields of comparatively simple configurations that admit analytical solution to the Dirac equation allow one to go beyond the perturbation the- ory by including fields of arbitrary strength and thereby consider extreme conditions, under which it is uncertain whether well-probed theories continue to be correct and where even most firmly established fundamental laws may be questioned. For this reason we believe that when approaching such problems it is important to be aware of the status of various encountered facts by clearly distinguishing, which of them reflect basic principles and which depend on an approximation or a model exploited in establishing them. In this paper we concentrate on an important problem belonging to this class, namely the behavior of real and virtual electromagnetic excitations of the vacuum filled with constant and homogeneous electric ( E ) and magnetic ( B ) fields that are superposed in such a way that the both field invariants F = ( B 2 − E $^{2}$) / 2 and G = ( B · E ) are different from zero. This makes the most general case of a constant in space and in time electromagnetic field, such that neither electric nor magnetic component can be eliminated from it by a Lorentz transformation, but a special reference frame always exists, where they are parallel or an- tiparallel. We shall avoid calling all these excitations photons , even when they are real and not virtual, because photons only make a massless subclass of all possible real excitations of the vacuum possessing the same quantum numbers as photons and supplying poles to the same photon Green function. In principle, the excitations are completely described using the effective Lagrangian, which, when differentiated upon the fields, generates all two- and many-excitation vertices. However, as far as calculations are concerned, the use of the effective Lagrangian is efficient only if its dependence on the space- and time-derivatives of the field strengthes is not taken into account. The results obtained in this way relate to the vanishing excitation momentum components k$_{µ}$ → 0 , µ = 1 , 2 , 3 , 0 , and correspond, if extended beyond this infrared limit, to dispersion curves that are straight lines passing through the origin in the plane of the 2