The extended Koopmans' theorem (EKT) is combined with the energy-derivative formalism for the one-and two-particle reduced density matrices. Such a combination produces a versatile methodology for calculations of ionization potentials and electron affinities that, being applicable to any level of electron correlation treatment,is more general than the equation-of-motion (EOM) formalism. General expressions for the Feynman-Dyson amplitude, the pole strength, and the one-particle reduced density matrix of the hole state are derived. Like the electron propagator theory (EPT), the present approach provides a one-electron description of the electron attachment-detachment processes that is advantageous from the interpretive point of view. Numerical tests show that EKT calculations are capable of affording ionization potentials with accuracy comparable to that of the EPT methods but at a substantially lower computational cost. (C) 1997 American Institute of Physics. [S0021-9606(97)03041-9].