In this paper,the long-term dependence phenomenon(the Hurst Effect) which characterizes hydrological and other geophysical times series is studied.The long-term memory is analysed for both daily and monthly streamflow series of the Benue River at Makurdi,Nigeria by using heuristic methods and testing specifically the null hypothesis of short-term memory in the monthly flow series.Results obtained by applying heuristic procedures indicated that there may be the presence of long-term memory component in mean daily flow series but there is no discernible reason to suspect the presence in both average monthly and maximum monthly flow series(extreme event).Hypothesis testing was conducted by using original and modified versions of rescaled range statistic.When the modified rescaled range,which accounts for short-term memory in the series,is used,the null hypothesis is accepted for both the average monthly and maximum monthly flow series,indicating little or no probable presence of long-term memory in the series.An identical conclusion is also arrived at when second null hypothesis for independence of the monthly flow series is tested.Therefore,apart from the mean daily flow series,there is little evidence of long-term dependence in the Benue River streamflow series at Makurdi.However,considering the limited length of data used,the results are inconclusive. In this paper, the long-term dependence phenomenon (the Hurst Effect) which characterizes hydrological and other geophysical times series is studied. Long-term memory is analysed for both daily and monthly streamflow series of the Benue River at Makurdi, Nigeria by using heuristic methods and testing specifically the null hypothesis of short-term memory in the monthly flow series. Results obtained by applying heuristic procedures indicated that there may be the presence of long-term memory component in mean daily flow series but there is no discernible reason to suspect the presence in both average monthly and maximum monthly flow series (extreme event). Hypothesis testing was conducted by using original and modified versions of rescaled range statistic. What is the modified rescaled range, which accounts for short-term memory in the series, is used, the null hypothesis is accepted for both the average monthly and maximum monthly flow series, indicating little or no probable presence of long-term memory in the series. An identical conclusion is also arrived at when second null hypothesis for independence of the monthly flow series is tested. Herefore, apart from the mean daily flow series, there is little evidence of long-term dependence in the Benue River streamflow series at Makurdi. Despite, considering the limited length of data used, the results are inconclusive.