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This study aimed to assess the changes in neonatal and infant mortality rates in Nigeria over the period 1990 to 2018 using Nigerian Demographic and Health Survey (NDHS) data, and assess their socio-demographic determinants using data from the most recent survey conducted in 2018. The infant mortality rate was 87 per 1000 live births in 1990, and this increased to 100 per 1000 live births in 2003 - an increase of around 15% over 13 years. Neonatal and infant mortality rates started to decline steadily thereafter and continued to do so until 2013. After 2013, neonatal morality rose slightly by the year 2018. Information for 27,465 infants under 1 year of age from the NDHS-2018 was analysed using bivariate and multivariate analysis and the Cox proportional hazard technique. In 2018, infant deaths decreased as wealth increased, and the incidence of infant deaths was greater among those of Islam religion than among those of other religions. A negative association was found between infant deaths and the size of a child at birth. Infant mortality was higher in rural than in urban areas, and was higher among male than female children. Both neonatal and infant death rates varied by region and were found to be highest in the North West region and lowest in the South region. An increasing trend was observed in neonatal mortality in the 5-year period from 2013 to 2018. Policy interventions should be focused on the poor classes, women with a birth interval of less than 2 years and those living in the North West region of the country. [ABSTRACT FROM AUTHOR]