This study aimed to examine the weak-form efficiency of some of the most capitalised cryptocurrencies. The sample consisted of 24 cryptocurrencies selected out of 30 cryptocurrencies with the highest market capitalisation as of October 19, 2022. Stablecoins were not considered. The study covered the period from January 1, 2018 to August 31, 2022. The results of robust martingale difference hypothesis tests suggest that the examined cryptocurrencies were efficient most of the time. However, their efficiency turned out to be time-varying, which validates the adaptive market hypothesis. No evidence was found for the impact of the coronavirus outbreak and the Russian invasion of Ukraine on the weak-form efficiency of the examined cryptocurrencies. The differences in efficiency between the most efficient cryptocurrencies and the least efficient ones were noticeable, but not large. The results also allowed to observe some slight differences in efficiency between the cryptocurrencies with the largest market cap and cryptocurrencies with the lowest market cap. However, the differences between the two groups were too small to draw any far-reaching conclusions about a positive relationship between the market cap and efficiency. The obtained results also did not allow us to detect any trends in efficiency.