A new method for determining the instants of significant excitation in speech signals is proposed. In the paper, significant excitation refers primarily to the instant of glottal closure within a pitch period in voiced speech. The method is based on the global phase characteristics of minimum phase signals. The average slope of the unwrapped phase of the short-time Fourier transform of linear prediction residual is calculated as a function of time. Instants where the phase slope function makes a positive zero-crossing are identified as significant excitations. The method is discussed in a source-filter context of speech production. The method is not sensitive to the characteristics of the filter. The influence of the type, length, and position of the analysis window is discussed. The method works well for all types of voiced speech in male as well as female speech but, in all cases, under noise-free conditions only.