The equation for the determination of the energy levels and wavefunctions of quasidegenerate states of the relativistic few-electron atom in the form of the usual eigenvalue problem for an energy operator (‘Schrodinger-like equation1) is constructed consistently from quantum electrodynamics (qed). Two choices of the space Ω2, in which the constructed energy operator H acts, are considered. In the first case Ω2 = Ω2 is the space of the fine structure levels. In the second case Ω2 = Ω2b is the space of all the positive energy states which correspond to the non-relativistic region of the spectrum. The construction of H in the Feynman gauge in the first and second (with the precision up to the terms α²(αZ)²m) orders in a is demonstrated for both choices of Ω . An effective expression for the energy operator Hcti, which gives the energy values within am for high Z and within α²(αZ)²m) for low Z, is proposed.