Abstract This paper aims to focus weekly stock market prices from the CEECs (Lithuania, Hungary, Romania, Croatia, Slovenia, Poland, Bulgaria, the Slovak Republic, Latvia, Estonia, and the Czech Republic) markets for evidence of weak-form market efficiency. This is complemented by the use of comprehensive unit root tests to test for abnormal return behaviour in these stock markets. For this purpose, Harvey et al. (2008) linearity test was applied in order to determine the characteristics of the series. The results indicate that the series with linear characteristics are Slovenia, Bulgaria, the Slovak Republic, Estonia, and the Czech Republic and those with non-linear characteristics are Lithuania, Hungary, Romania, Croatia, Poland, and Latvia. Then, in order to examine the weak-form market efficiency, DF-GLS (1996), Phillips-Perron (1988) and Lee-Strazicich (2003) unit root tests are applied to linear series and Kapetanios et al. (2003) and Kruse (2011) tests were applied to nonlinear series. The linear and nonlinear unit root tests evidence that all the selected stock markets in CEECs have a unit root, in other words, are non-stationary. In the period analyzed, the results suggest that the weak-form efficient market hypothesis holds in the CEECs. Accordingly, the results indicate support for the validity of the random walks hypothesis in all the selected stock markets in CEECs. It means that investors should not be able to earn abnormal returns by carrying out the same analysis and analysing historical prices in CEECs. The finding of weak-form market efficiency has notable implications from the point of capital allocation, stock price predictability, and the influence of shocks to stock prices.