This paper examines the risk connectedness across seven cryptocurrencies, Bitcoin, Ethereum, Ripple, Litecoin, Stellar, Monero, and Dash, which have large capitalizations in the cryptocurrency market. The data sample is from August 7, 2015, to February 15, 2020. We measure the return risks of the cryptocurrencies by using the CAViaR model, showing that they have similar risk tendencies, with volatility clusterings from the beginning of 2017 to the end of 2018. The net pairwise spillover index developed by Diebold and Yilmaz [1] is used as the measure of the risk connectedness among the cryptocurrencies. We find that the risk spillover directions are highly correlative with the market capitalizations of the cryptocurrencies. Cryptocurrencies with small market capitalization transmit risks to those with large market capitalization. When there is a downward risk tendency, the risk spillover levels among the cryptocurrencies are stronger than when there is an upward risk tendency, while the spillover directions remain the same under both risk tendencies, except for the cryptocurrency Monero, the particularity of which may be due to the difference in its trading volume compared to the others. We use generalized forecast error variance decomposition for the spillover index and explore the risk connectedness across the cryptocurrencies at different timescales, namely, the short term (0-4 days), medium term (4-30 days) and long term (30-300 days). The risk spillovers can be neglected at the short-term frequency, which implies a delayed effect. The risk spillovers at medium-term frequency are mostly stronger than those at long-term frequency. The dynamic connectedness results show that the means of risk spillover at a long-term frequency are larger than those at medium-term frequency. An inverse result holds for the ranges of risk spillover. The fluctuations of risk spillover at long-term and medium-term frequencies admit the same comparison result with the means of risk spillover in these two frequencies. The findings in this paper provide some suggestions for regulators controlling market stability and cryptocurrency investors generating investment strategies.