The hypernasality in cleft palate speech is characterized by the presence of nasal peak in the vicinity of first formant of vowel spectrum. A high spectral resolution technique, which can resolve these two peaks, is desirable for the automatic detection of hypernasality. This work uses the zero time windowing (ZTW) technique for the hypernasality detection. In this technique, the speech signal is windowed with a highly decaying impulse-like window of approximately a pitch period size. The technique gives the instantaneous vocal tract spectrum free from the pitch and harmonics effect. The spectral resolution loss due to short windowing is restored by the successive differentiation in frequency domain. The numerator of group delay is used to resolve closely spaced nasal peak and first formant. The cepstral feature is extracted from the instantaneous spectrum and is used for the automatic detection of hypernasality using SVM classifier. The accuracy of classification are 76.51% for the vowel /a/ and 80.36% for the vowel /i/. The accuracy further increases when the proposed feature is fused at score level with the Mel-frequency cepstral coefficient (MFCC) feature. © 2018 IEEE.