A systematic theoretical study of the reactions of HO2 with RO2 has been carried out. The major concern of the present work is to gain insight into the reaction mechanism and then to explain experimental observations and to predict new product channels for this class of reactions of importance in the atmosphere. In this paper, the reaction mechanisms for two reactions. namely, HO2 + CH3O2 and HO2 + CH2FO2, are reported. Both singlet and triplet potential energy surfaces are investigated. The complexity of the present system makes it impossible to use a single ab initio method to map out all the reaction paths. Various ab initio methods including MP2, CISD. QCISD(T) CCSD(T) CASSCF. and density function theory (B3LYP) have been employed with the basis sets ranging from 6-31G(d) to an extrapolated complete basis set (CBS) limit. It has been established that the CCSD(T)/cc-pVDZ//B3LYP/6-311G(d,p) scheme represents the most feasible method for our systematic study. For the HO2 + CH3O2 reaction, the production of CH3OOH is determined to be the dominant channel. For the HO2 + CH2FO2 reaction, both CH2FOOH and CHFO are major products, whereas the formation of CHFO is dominant in the overall reaction. The computational findings give a fair explanation for the experimental observation of the products.