Abstract Memory T-cell responses following SARS-CoV-2 infection have been extensively investigated but many studies have been small with a limited range of disease severity. Here we analyze SARS-CoV-2 reactive T-cell responses in 768 convalescent SARS-CoV-2-infected (cases) and 500 uninfected (controls) Icelanders. The T-cell responses are stable three to eight months after SARS-CoV-2 infection, irrespective of disease severity and even those with the mildest symptoms induce broad and persistent T-cell responses. Robust CD4 + T-cell responses are detected against all measured proteins (M, N, S and S1) while the N protein induces strongest CD8 + T-cell responses. CD4 + T-cell responses correlate with disease severity, humoral responses and age, whereas CD8 + T-cell responses correlate with age and functional antibodies. Further, CD8 + T-cell responses associate with several class I HLA alleles. Our results, provide new insight into HLA restriction of CD8 + T-cell immunity and other factors contributing to heterogeneity of T-cell responses following SARS-CoV-2 infection.