Cryptocurrency price prediction is a crucial task for financial investors as it helps determine appropriate investment strategies and mitigate risk. In recent years, deep learning methods have shown promise in predicting time-series data, making them a viable approach for cryptocurrency price prediction. In this study, we compare the effectiveness of two deep learning techniques, the Recurrent Neural Network (RNN) and Long-Short Term Memory (LSTM), in predicting the prices of Bitcoin and Ethereum. Results of this research show that the LSTM method outperformed the RNN method, obtaining lower Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) values for predicting both cryptocurrencies. Bitcoin and Ethereum. Specifically, the LSTM model had a RMSE of 0.061 and MAPE of 5.66% for predicting Bitcoin, and a RMSE of 0.036 and MAPE of 4.58% for predicting Ethereum. In this research, we found that the LSTM model is a more effective method for predicting cryptocurrency prices than the RNN model.