The equation-of-motion (EOM) method and the equivalent superoperator propagator approach, used in studies of (generalized) electronic excitations, are analyzed with respect to two basic properties referred to as separability and compactness. The separability property ensures that the computed excitation energies and transition moments are size consistent; compactness means that the secular configuration spaces used in the EOM and propagator schemes can be systematically smaller than those of comparable configuration-interaction (CI) expansions. The validity of these properties depends critically on an appropriate orthonormalization of the operator manifolds used in the EOM and propagator schemes. Separable and compact EOM versions are obtained by generalizing the excitation class orthogonalization procedure discussed in the preceding paper [Phys. Rev. A 53, 2140 (1996)] to the basis operators. Moreover, it is shown that the EOM secular equations for N\ifmmode\pm\else\textpm\fi{}1,N\ifmmode\pm\else\textpm\fi{}2,..., electron systems can be formulated as state representations of a generalized Hamiltonian in terms of ``intermediate'' Fock space states. These intermediate-state representations (ISR's) give some interesting insight complementing the usual operator based derivation of the EOM propagator schemes. In particular, the ISR formulation allows for a transparent discussion of the relationship between the (N\ifmmode\pm\else\textpm\fi{}1)-electron EOM scheme and the Dyson equation for the electron propagator. Some potentially useful EOM variants are proposed. \textcopyright{} 1996 The American Physical Society.