Detection of seizures in neonatal EEG signal represents a formidable challenge for clinicians in the neonatal intensive care unit (NICU). Seizure morphology is known to evolve both temporally and spatially with a similar evolution also observed in the frequency domain. The modulation frequency analysis which is widely used in speech processing is used here to extract the frequency-localized spectral dynamics of the neonatal EEG and investigate their discriminative capabilities in the context of neonatal seizure detection. This study suggests that the spectral dynamics of neonatal EEG are more informative than short-term spectral characteristics. It is shown that the seizure-relevant components of the modulation spectrogram are found in the vicinity of 0.4Hz. Modulation frequency analysis represents a new insight into the EEG signal which can uncover the underlying time-structural organization of the neonatal EEG signal and therefore improve clinical understanding of the dynamic processes involved.