Background: In recent studies, up to half of immunocompromised (IC) subject populations fail to develop antibodies after COVID-19 vaccination. Purpose and Methods: Here, we explore whether T-cells which respond to the spike (S) antigenic sequence and its less conserved S1, and the conserved S2 component are present in serial samples before and after each dose of mRNA1273 or BNT162b2 vaccines in 20 healthy immunocompetent subjects. Single samples from 7 vaccinated IC subjects were also tested. Simultaneously, we measured IgG antibodies to the receptor binding domain (RBD) of S1, and anti-S IgG, and frequencies of monocytic CD14+HLA-DR- (M-MDSC) and polymorphonuclear CD14-CD15+CD11b+ (PMN-MDSC) myeloid-derived suppressor cells. Results: In healthy subjects, S1-, S2-, and S-reactive CD4 and CD8 T-cell frequencies showed a numeric but not statistically significant decrease after the first vaccine dose and were accompanied by increased MDSC frequencies (p<0.05). After the second dose, S2- and S-reactive CD4 and CD8 cells and MDSC approached pre-vaccination levels. In healthy subjects, a) S1-reactive CD8 frequencies were significantly higher after the second dose compared with pre-vaccination levels (p=0.015), b) anti-RBD and anti-S IgG were present in all after the second dose. Among seven IC subjects, anti-RBD and anti-S IgG were absent in 4 and 3 subjects, respectively. S1-reactive CD8 cells were identified in 2 of 4 anti-RBD negative subjects. S-reactive CD4 or CD8 cells were identified in all three anti-S negative subjects. Conclusions: In healthy immunocompetent subjects, mRNA vaccines induce antibodies to the spike antigenic sequences and augment CD8 cells reactive to the S1 spike sequence, which is more specific for the SARS-CoV-2 virus. In this exploratory cohort of vaccinated immunocompromised subjects, S1-reactive CD8 cells can be detected in some who are negative for RBD antibody, and S-reactive T-cells are present in all who are negative for spike antibody.