Four common human coronaviruses, HCoV-OC43, HCoV-229E, HCoV-NL63, and HCoV-HKV1, circulate among the global population, but are comparatively less dangerous than SAR-CoV-2 6. We hypothesized that a cross-response of cytotoxic cells 7, selected during an immune response to these common viruses, may play an auxiliary role during elimination of SARS-CoV-2. Unfortunately, T-lymphocyte responses are much more difficult to study in vitro than B-lymphocyte responses. To this end, and because of the importance of T-cells during viral infections, we focused on the T-cell response 7. We tested the above hypothesis using in silico models. We assumed that the MHC I peptides were properly selected during our in silico studies. Next, we performed a search for identical, or nearly identical, peptides presented by MHC I molecules during infection with the four common human coronaviruses and SARS-CoV-2. Our in silico analysis suggests that T lymphocytes selected during infection with the mild coronaviruses exhibit cross-reactivity with SARS-CoV-2, as they share antigenic peptides with SARS-CoV-2 peptides. Indeed, several SARS-CoV-2 proteins share peptides/epitopes with HCoV-HKU1 HCoV-OC43, HCoV-229E, and HCoV-NL63, including epitopes from helicase, RNA polymerase, proofreading exoribonuclease, and 2'-O-methyltransferase. Importantly, these molecules are not virion surface proteins and are not optimal targets for antibodies. We are aware of the many limitations in the use of in silico testing to predict which peptides are recognized/presented after infection 8,9. However, the number of common peptides identified in this study was relatively large, and the common epitopes were found in all four mild coronaviruses. Therefore, it cannot be ruled out that T-cell cross-reactivity may offer some protection against SARS-CoV-2 for people who have been infected with other, less dangerous coronaviruses; a similar conclusion was recently published 10. Therefore, we suggest that the T-lymphocytes selected and expanded during infection with SARS-CoV-2, as well as cross-reactive T-lymphocytes propagated during mild coronavirus infections, can support the immune response to SARS-CoV-2.