We test whether the selected cryptocurrencies exhibit long memory behavior in returns and volatility. We use data on five most traded cryptocurrencies: Bitcoin, Litecoin, Ethereum, Bitcoin Cash, and XRP. Using recent tests of long memory developed against persistent and nonlinear alternatives, this paper finds that long memory is mostly rejected in returns. The tests fail to reject the null hypothesis of long memory in most cases across different volatility proxies and cryptocurrencies. The estimated memory parameters show that volatility is persistent, and when volatility is measured by log range, it is borderline nonstationary.