Host cells can detect virus infections and respond by inducing defense programs to suppress viral replication and spread. One of such antiviral mechanisms is the formation of stress granules, which are the concentrated foci of RNA and proteins that can sequester viral and cellular factors needed for viral replication. Accordingly, viruses often possess mechanisms that prevent stress granule formation. Studying these mechanisms can reveal new targets for therapies that would disable viral countermeasures and render cells resistant to infection. In this study, we analyzed inhibition of stress granules by two human coronaviruses: the common cold coronavirus OC43 and the pandemic SARS-CoV2. We discovered that these viruses possess two proteins that block stress granule formation through distinct complementary mechanisms. In addition, we found that the non-structural protein 1 (Nsp1) of SARS-CoV2 inhibits stress granule formation by causing degradation of cellular cytoplasmic messenger RNAs – one of the major constituents of stress granules. Existence of multiple mechanisms of stress granule inhibition in coronaviruses indicates that counteracting this antiviral response is crucial for productive virus infection.