This article deals with the modelling of growth rate time series in Nigeria with a view of detecting its statistical properties, structural breaks and non-linearities. We employ both fractional integration and structural break time series techniques in modelling the annual growth rate series of the Nigerian GDP growth rate for about 55 years. The data span between 1960 and 2017. The results show that Nigerian growth rate is unstable with non-linearities and long-range dependence structures. We also investigate what might explain these features and conclude that erratic political institutions, associated with poor economic management and insecurity in Nigeria, among others, in the decades after independence are the root causes of non-linearities observed, which have also led to the subsequent recent economic recession in Nigeria.