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This letter proposes a time-effective method for determining the instants of significant excitation in speech signals. The instants of significant excitation correspond to the instants of glottal closure (epochs) in the case of voiced speech, and to some random excitations like onset of burst in the case of nonvoiced speech. The proposed method consists of two phases: the first phase determines the approximate epoch locations using the Hilbert envelope of the linear prediction residual of the speech signal. The second phase determines the accurate locations of the instants of significant excitation by computing the group delay around the approximate epoch locations derived from the first phase. The accuracy in determining the instants of significant excitation and the time complexity of the proposed method is compared with the group delay based approach.