The electroencephalogram (EEG), used to noninvasively monitor brain activity, remains the most reliable tool in the diagnosis of neonatal seizures. Due to their nonstationary and multi-component nature, newborn EEG seizures are better represented in the joint time-frequency domain than in either the time domain or the frequency domain. Characterising newborn EEG seizure nonstationarities helps to better understand their time-varying nature and, therefore, allow developing efficient signal processing methods for both modelling and seizure detection and classification. In this article, we used the instantaneous frequency (IF) extracted from a time-frequency distribution to characterise newborn EEG seizures. We fitted four frequency modulated (FM) models to the extracted IFs, namely a linear FM, a piecewise-linear FM, a sinusoidal FM, and a hyperbolic FM. Using a database of 30-s EEG seizure epochs acquired from 35 newborns, we were able to show that, depending on EEG channel, the sinusoidal and piecewise-linear FM models best fitted 80-98% of seizure epochs. To further characterise the EEG seizures, we calculated the mean frequency and frequency span of the extracted IFs. We showed that in the majority of the cases (>95%), the mean frequency resides in the 0.6-3 Hz band with a frequency span of 0.2-1 Hz. In terms of the frequency of occurrence of the four seizure models, the statistical analysis showed that there is no significant difference (p = 0.332) between the two hemispheres. The results also indicate that there is no significant differences between the two hemispheres in terms of the mean frequency (p = 0.186) and the frequency span (p = 0.302).