The notion of absolute efficiency has been challenged in the recent time with the advent of Adaptive Market Hypothesis (AMH) which debunked the idea of viewing efficiency as all or nothing phenomenon. This study investigated the Adaptive Market Hypothesis in the Nigerian stock market. Three return frequencies of All Share Index from 2000-2017 were employed in this study. Various tests (unit root, autocorrelation, variance ratio, run and BDS tests) of linear and nonlinear dependence in stock returns were carried out using the new overlapping sub-period methodology. The study employed 2-years sub-periods pushed forward by one year. The process was repeated until Dec 2017 and generated about 17 windows. The hypothesis for each of the tests was tested for each window so as to determine how windows of dependence and independence vary over time in Nigerian Stock market. Considering the linear dependence tests namely the unit root, autocorrelation, variance ratio and run test, this study found that there are more sub-periods of linear dependence than independence, hence the market is said to be adaptively inefficient. In case of the nonlinear dependence test of BDS, this study also found that there are more sub-periods of nonlinear dependence than independence, confirming the market is adaptively inefficient. This implies that the Nigeria stock market follows the Adaptive Market Hypothesis as revealed by the three frequencies of return data. We found out that the Nigerian stock exchange cannot be described as inefficient and the best way to describe the market is adaptively inefficient. The implication for market participants is that the Nigerian stock market should be viewed as adaptively inefficient. This implies that the profitability of trading strategies may vary over time. We therefore recommend that the government policies should be reviewed as at when due because it is one of the market conditions that determined the efficiency in the stock market since the market efficiency changes over time as market condition changes. Researcher should investigate sectors of NSE using AMH approach. JEL Classification: G12 and G15. Keywords: Market Efficiency, Stock Returns, Adaptive Market Hypothesis, overlapping sub-period, Linear Test, Nonlinear tests. NSE.