SARS-CoV-2 has been identified as the causative agent of a global outbreak of respiratory tract disease (COVID-19). In some patients the infection results in moderate to severe acute respiratory distress syndrome (ARDS), requiring invasive mechanical ventilation. High serum levels of IL-6, IL-10 and an immune hyperresponsiveness referred to as a 'cytokine storm' have been associated with poor clinical outcome. Despite the large numbers of COVID-19 cases and deaths, information on the phenotype and kinetics of SARS-CoV-2-specific T cells is limited. Here, we studied 10 COVID-19 patients who required admission to an intensive care unit and detected SARS-CoV-2-specific CD4+ and CD8+ T cells in 10 out of 10 and 8 out of 10 patients, respectively. We also detected low levels of SARS-CoV-2-reactive T cells in 2 out of 10 healthy controls not previously exposed to SARS-CoV-2, which is indicative of cross-reactivity due to past infection with 'common cold' coronaviruses. The strongest T-cell responses were directed to the spike (S) surface glycoprotein, and SARS-CoV-2-specific T cells predominantly produced effector and Th1 cytokines, although Th2 and Th17 cytokines were also detected. Furthermore, we studied T-cell kinetics and showed that SARS-CoV-2-specific T cells are present relatively early and increase over time. Collectively, these data shed light on the potential variations in T-cell responses as a function of disease severity, an issue that is key to understanding the potential role of immunopathology in the disease, and also inform vaccine design and evaluation.