A procedure is presented for using available molecular data to compute the activation energies and rate constants of bimolecular transfer reactions for the halogen atoms. This computational method is also applied to calculating the kinetics for transfers of O, N, C, B, Be, and Al atoms bonded to univalent atoms. The procedure is based on modifications of the Johnston-Parr method of predicting kinetic data for hydrogen-atom transfer reactions. Potential energies of repulsion are calculated by using a reduced variable treatment of the Sato function. The procedure and results are also presented for computations of high-temperature rates of hydrogen-atom transfer reactions in which molecules containing a total of four atoms are involved. Computed rate constants are compared with experimental kinetic data when available, and agreement is generally satisfactory. Less than 0.1 minute of electronic-computer time per reaction is required to calculate the activation energy, vibrational parameters of the activated complex, rate constants at 25 temperatures (primarily in the 1000° to 4000°K range), and Arrhenius rate equation constants. Results are summarized for bimolecular atom-transfer reactions involving combustion products such as HF, HCl, HBr, HI, CF, CCl, BF, BCl, BeCl, ClO, AlCl, CH, OH, NH, AlH, BH, BeH, CH2, NH2, BH2, BeH2, H2O, HCO, HBO, HCN, AlOH, and NaOH.