Present doctoral thesis contributed to understanding of mechanistic principles of two enzymes participating in the process of carcinogenesis; DNA polymerase  (pol ) and cytochromes P450 (CYP). Pol  is part of the DNA base-excision repair mechanism (BER). The primary role of pol  in, the BER mechanism, is inserting a new nucleotide into a DNA strand according to Watson-Crick base pairing rules. Pol  plays an important role in the process of carcinogenesis, approximately 30 % of human tumors express pol  mutants. The ability of pol  to discriminate between "right" and "wrong" nucleotide during the insertion process is called fidelity. We employed computational methods to elucidate molecular basis of the fidelity of pol . First, the relative free energy calculation method LRA was employed to compare differences in free energies between the "right" and "wrong" nucleotide during its insertion into DNA. The results indicated a better stabilization of transition-state of the nucleophilic substitution catalyzed by pol  in the case of the "right" versus "wrong" nucleotide. This difference resulted in an 80-fold contribution to its fidelity. Further, computational methods FEP and LIE were used to examine how mutations effect fidelity of pol . Results were than correlated with experimental data...