This study explores the bubble behavior in the prices of top five cryptocurrencies (i.e., Bitcoin, Ethereum, Ripple, Stellar, and Tether) using daily data of the closing level at the COVID-19 pandemic, covering the period from January 2, 2020 to January 2, 2021. The testing procedure of the bubble behavior in selected cryptocurrency prices is investigated by two methodologies, which are rarely applied in the relevant literature. Those covers the test statistics originated by the Supremum Augmented Dickey-Fuller (SADF) (Phillips et al., 2011) and Generalized Supremum Augmented Dickey-Fuller (GSADF) (Phillips et al., 2015) to define several bubble periods. The empirical results emphasize that bubble behavior is not a diverse and stable feature of Bitcoin, Ethereum, Ripple, and Stellar prices, except the Tether prices, which point out the emergence of a potential crisis in the digital assets market through an increasing degree of financial instability.