This paper deals with the analysis of the relationship between oil prices and the stock market in Nigeria. We focus on measuring the degree of persistence of the series using long range dependence techniques, and based on the similarities observed between the two series, a fractionally cointegrated modeling framework is proposed. The results first indicate that the two series display a similar order of integration, which is close to, although above 1. Testing the hypothesis of cointegration, this is decisively rejected since the order of integration in the potential equilibrium relationship was similar to that of the parent individual series. However, testing a long memory model with oil prices acting as a weakly exogenous regressor, we obtained significant evidence of a positive relationship between the two variables though with a very short memory effect, this relation being significant only during the following three months.