Telephone speech is one of the degradations involved in building speech systems in practical environments. The potential use of the speech systems depends on the speech analysis algorithms that can handle different acoustic variations and degradations often found in the human speech communication. Detection of epochs/glottal closure instants (GCIs) is typically required in such analysis stages. In this paper, the effect of telephone channel speech on the accuracy of detection of epochs using state-of-art epoch extraction methods is investigated. Epoch is the instant of significant excitation to the vocal tract system in voiced speech. Most of the existing epoch extraction algorithms are shown to perform excellently well on the speech data collected under lab environment. The efficiency of these algorithms for the analysis of telephone quality speech is quantitatively studied and the strengths and weaknesses of the methods are discussed here. The methods are evaluated on six large databases containing speech and simultaneous EGG recordings as the ground truth. The state-of-art epoch extraction algorithms considered in this study for comparison are: ZFF, YAGA, DYPSA, SEDREAMS, SE-VQ and MMF. The performance of the algorithms is evaluated in terms of both reliability and accuracy measures.