Bitcoin, a decentralized digital currency based on cryptographic principles, has aroused great interest globally due to its rapid rise in recent years and certain qualities such as limited supply. Therefore, the foundations, economic consequences and social effects of blockchain technology have become one of the leading topics of academic research. This study aims to investigate the time series properties of Bitcoin (BTC) and Ethereum (ETH) prices and the bubble behaviors exhibited by these prices, using weekly data for the 2015-2023 period. For this purpose, a two-step estimation procedure was followed in the study. In the first stage, time series properties such as stationarity and structural break of the related series are examined. The findings reveal that BTC and ETH cryptocurrencies have been subject to multiple structural breaks during the period and the effects of shocks to the variables tend to be temporary. In the second step, the bubble behaviors of these digital assets were analyzed by using the GSADF test proposed by Phillips vd. (2013). The GSADF test results indicate two main bubble periods, as well as several short-lived bubble periods for BTC prices. The first of these main bubbles corresponds to the period from January 2017, when BTC price exceeded $ 1,000, to the period of January 2018, when it approached $ 20,000, and the second corresponds to the first half of 2021, when BTC price approached $ 60,000. The GSADF test also identified a short-term bubble period in the first week of December 2021, when BTC price reached its historical peak at $67,500. It can be said that the periods when ETH exhibited bubble behaviors largely coincided with BTC bubbles; however, it should be noted that these bubbles tend to be of shorter duration compared to BTC bubbles. As a result, policymakers need to reassess regulatory frameworks to manage the risks associated with price bubbles frequently seen in cryptocurrencies. These frameworks may include implementing measures to improve market transparency, investor protection, and risk management practices in the cryptocurrency ecosystem.