This paper deals with the analysis of the stock market prices in Nigeria from 1987 to 2017. The results indicate little evidence of mean reversion since most of orders of integration are equal to or higher than 1. The possibility of structural breaks is also examined and the results indicate the existence of two break, at 1996M1 and at 2005M1. We observe that for the first subsample the unit root hypothesis cannot be rejected; however, for the remaining two sub-periods, the I(1) hypothesis is rejected in favor of d > 1. Thus, we observe an increase in the degree of persistence across the subsamples in the study. The break dates discovered coincide with the period of high inflation in Nigeria which may suggest a relationship between economic development and the stock price index in the country.