The market for cryptocurrencies has experienced extremely turbulent conditions in recent times, and we can clearly identify strong bull and bear market phenomena over the past year. In this paper, we utilise algorithms for detecting turnings points to identify both bull and bear phases in high-frequency markets for the three largest cryptocurrencies of Bitcoin, Ethereum, and Litecoin. We also examine the market efficiency and liquidity of the selected cryptocurrencies during these periods using high-frequency data. Our findings show that the hourly returns of the three cryptocurrencies during a bull market indicate market efficiency when using the detrended-fluctuation-analysis (DFA) method to analyse the Hurst exponent with a rolling window. However, when conditions turn and there is a bear-market period, we see signs of a more inefficient market. Furthermore, our results indicated differences between the cryptocurrencies in terms of their liquidity during the two market states. Moving from a bull to a bear market, Ethereum and Litecoin appear to become more illiquid, as opposed to Bitcoin, which appears to become more liquid. The motivation to study the high-frequency cryptocurrency market came from the increasing availability of higher-frequency cryptocurrency-pricing data. However, it also comes from a movement towards higher-frequency trading of cryptocurrency. In addition, the efficiency of cryptocurrency markets relates not only to whether prices are predictable and arbitrage opportunities exist, but, more widely, to topics such as testing the profitability of trading strategies and determining the maturity of cryptocurrency markets.