The dominating electron-electron interactions which characterize the spectrum of a quasi-two-electron atom will be examined. A brief review will be presented first following the results of a systematic application of a simple configuration interaction (CI) calculational procedure for Mg atom and its corresponding isoelectronic sequence on i) the energy levels, ii) the oscillator strengths, iii) the fine-structure level splittings, iv) the resonance energy and the width of the doubly excited autoionization states, and v) the photoionization dominated by those doubly excited autoionization states. In spite of the good quantitative agreement between the results of this simple CI calculation and the available observed data, the accuracy of the theoretical estimation can be further improved by replacing the incomplete bound basis set in the CI calculation with a quasicomplete basis set constructed from B splines. The substantially improved numerical accuracy of this modified CI procedure is demonstrated in its application to the determination of the energy levels, the oscillator strengths, and the excitation energies of Be atom.