Human X-family DNA polymerases beta (Pol beta) and lambda (Pol lambda) catalyze the nucleotidyl-transfer reaction in the base excision repair pathway of the cellular DNA damage response. Using empirical valence bond and free-energy perturbation simulations, we explore the feasibility of various mechanisms for the deprotonation of the 3'-OH group of the primer DNA strand, and the subsequent formation and cleavage of P-O bonds in four Pol beta, two truncated Pol lambda (tPol lambda), and two tPol lambda Loop1 mutant (tPol lambda Delta L1) systems differing in the initial X-ray crystal structure and nascent base pair. The average calculated activation free energies of 14, 18, and 22 kcal mol(-1) for Pol beta, tPol lambda, and tPol lambda Delta L1, respectively, reproduce the trend in the observed catalytic rate constants. The most feasible reaction pathway consists of two successive steps: specific base (SB) proton transfer followed by rate-limiting concerted formation and cleavage of the P-O bonds. We identify linear free-energy relationships (LFERs) which show that the differences in the overall activation and reaction free energies among the eight studied systems are determined by the reaction free energy of the SB proton transfer. We discuss the implications of the LFERs and suggest pK(a) of the 3'-OH group as a predictor of the catalytic rate of X-family DNA polymerases.