Enormous efforts have been made worldwide to generate therapeutic options to prevent the transmissibility of the SARS-CoV-2 and reduce its replication in humans. Currently, the emergence of new variants of the virus is of great concern because the evolution of the viral genome and the inherent mutations introduced in the viral proteins could decrease the effectiveness of the first line therapeutic agents used to prevent and treat COVID-19. The present study evaluated the susceptibility of two important pharmacological drug targets of SARS-CoV-2, the major protease (Mpro) and the RNA-dependent RNA polymerase (RdRp), to suffer point mutations that could produce resistance to inhibitors of these enzymes. The results showed that the residues that contour the inhibitor binding site in RdRp are extremely conserved between the different RNA virus species. This suggests the RdRp enzyme has a low probability to suffer mutation that could confer resistance to therapeutic drugs, such as remdesivir, an FDA approved compound to treat COVID-19. In contrast, we observed that the Mpro enzyme could undergo up to ten-point mutations in the active site, which is the binding site of several experimental drugs under development, such as Carmofur and N3. Molecular docking analysis showed that the presence of single point mutations in the Mpro active site produces an increase in the binding affinity of carmofur, probably due to the small size and high flexibility of this molecule. However, the Pro168Ser and Ala191Val mutations significantly decrease the affinity of N3 binding to Mpro, suggesting the possible emergence of resistance to this drug. These results could help to anticipate the effect of different mutations on the way Mpro inhibitors bind to the enzyme, and design new inhibitors that address the effect of resistance.Enormous efforts have been made worldwide to generate therapeutic options to prevent the transmissibility of SARS-CoV-2 and reduce its replication in humans. Currently, the emergence of new variants of the virus is of great concern because the evolution of the viral genome and the inherent mutations introduced in the viral proteins could decrease the effectiveness of the first-line therapeutic agents used to prevent and treat COVID-19. The present study evaluated the susceptibility of two important pharmacological drug targets of SARS-CoV-2, the major protease (Mpro) and the RNA-dependent RNA polymerase (RdRp), to suffer point mutations that could produce resistance to inhibitors of these enzymes. The results showed that the residues that contour the inhibitor binding site in RdRp are extremely conserved between the different RNA virus species. This suggests the RdRp enzyme has a low probability to suffer mutation that could confer resistance to therapeutic drugs, such as Remdesivir, an FDA approved compound to treat COVID-19. In contrast, we observed that the Mpro enzyme could undergo up to ten-point mutations in the active site, which is the binding site of several experimental drugs under development, such as Carmofur and N3. Molecular docking analysis showed that the presence of single point mutations in the Mpro active site produces an increase in the binding affinity of carmofur, probably due to the small size and high flexibility of this molecule. However, the Pro168Ser and Ala191Val mutations significantly decrease the affinity of N3 binding to Mpro, suggesting the possible emergence of resistance to this drug. These results could help to anticipate the effect of different mutations on the way Mpro inhibitors bind to the enzyme, and design new inhibitors that address the effect of resistance.