Two new methods for the detection of the instant of glottal closure directly from the speech waveform are presented here. Both detect the abrupt changes in the short-term spectral characteristics of the speech signal within a pitch period caused by glottal events. The same statistical approach of sequential detection of events by hypothesis testing is used for this purpose. The first method is based on the maximization of a likelihood ratio, the second one uses a divergence convexity test. Experiments on real speech demonstrate the improved robustness of these methods.