Speakers with defective velopharyngeal mechanism, produce speech with inappropriate nasal resonances across vowel sounds. The acoustic analysis on hypernasal speech and nasalized vowels of normal speech shows that there is an additional frequency introduced in the low frequency region close to the first formant frequency . The conventional formant extraction techniques may fail to resolve closely spaced formants. In this paper, an attempt is made to use the group delay based algorithm  for the extraction of formant frequencies from hypernasal speech. Preliminary experiments on synthetic signal with closely spaced formants show that the formants are better resolved in group delay spectrum when compared to conventional methods. But when formants are too close with wider bandwidths, the group delay algorithm also fails to resolve prominently. This is primarily because of the influence of the other resonances in the signal. To extract the additional frequency close to the first formant, the speech signal is low-pass filtered and the formants are extracted using group delay function. Following the satisfactory results on synthetic signal, the above technique is used to extract formants from phonations /a/, /i/, and /u/ uttered by 15 speakers with cleft palate who are expected to produce hypernasal speech. Invariably in all the tests, an additional nasal resonance around 250 Hz and first formant frequency of vowels are resolved properly.