This study describes a new C-H bond activation pathway during CH4-CO2 reactions on oxophilic Ni-Co and Co clusters, unlike those established previously on Ni clusters. The initial C-H bond activation remains as the sole kinetically relevant step on Ni-Co, Ni, and Co clusters, but their specific reaction paths vary. On Ni clusters, C-H bond activation occurs via an oxidative addition step that involves a three-center (H3C···*···H)⧧ transition state, during which a Ni-atom inserts into the C-H bond and donates its electron density into the C-H bond's antibonding orbital. Ni-Co clusters are more oxophilic than Ni; thus, their surfaces are covered with oxygen adatoms. An oxygen adatom and a vicinal Co-atom form a metal-oxygen site-pair that cleaves the C-H bond via a σ bond metathesis reaction, during which the Co inserts into the C-H bond while the oxygen abstracts the leaving H-atom in a concerted, four-center (H3C···*···H···O*)⧧ transition state. Similarly, Co clusters also catalyze the σ bond metathesis step, but much less effectively because of their higher oxophilicities, much stronger binding to oxygen, and less effective hydrogen abstraction than Ni-Co clusters. On Ni-Co and Co clusters, the pseudo-first-order rate coefficients are single-valued functions of the CO2-to-CO ratio (or H2O-to-H2 ratio), because this ratio prescribes the oxygen chemical potentials and the relative abundances of metal-oxygen site-pairs through the water-gas shift equilibrium. The direct involvement of reactive oxygen in the kinetically relevant step leads to more effective CH4 turnovers and complete elimination of coke deposition on Ni-Co bimetallic clusters.