Time series analysis of Nigerian Stock Prices Data is done. The data used is monthly from 1987 to 2006. The time plot reveals a negative trend and no clear seasonality. A multiplicative seasonal model is suggestive given seasonality that tends to increase with time. Seasonal differencing once produced a series with a slightly positive trend but still with no discernible stationarity. A non-seasonal differencing of the seasonal differences yielded a series with no trend but with a correlogram revealing stationarity of order 12 and a seasonal moving average component . A multiplicative seasonal autoregressive integrated moving average (ARIMA) model, (0, 1, 1)x(0, 1, 1)12, is fitted to the series.