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This research explores the impact of COVID-19-related media coverage on the dynamic return and volatility connectedness of the three dominant cryptocurrencies (Bitcoin (BTC), Ethereum (ETH) and Ripple (XRP)) and the fiat currencies of the euro, GBP and Chinese yuan. The sample period covers the first and second devasting waves of the COVID-19 pandemic crisis and ranges from January 1, 2020, to December 31, 2020. The dynamic return and volatility connectedness measures are estimated using the time varying parameter-VAR approach. Our return connectedness analysis shows that the media coverage index (only before the first wave) and the cryptocurrencies are the net transmitters of shocks while the fiat currencies are the net receivers of shocks. Similar results are obtained in terms of volatility, except for the euro, which shows a clear net receiver profile in January and February. This fiat currency (the euro) became a net transmitter in March and during the first wave of the COVID-19 crisis, which possibly shows the virulence of the pandemic on the European continent. Moreover, the most relevant differences between the net dynamic (return and volatility) connectedness of these two groups of currencies are focused on the beginning of the sample period, just before the first wave of the SARS-CoV-2 pandemic crisis, although some differences are observed during the first and second waves of the coronavirus outbreak.