We derive a unified description of the low-energy elastic, inelastic, neutron transfer, and fusion cross sections of systems involving two stable oxygen isotopes. Coupled channels equations with an incoming wave boundary condition are employed, as is the no-recoil approximation; the adiabatic approximation, which violates unitarity, is avoided. A calculation with phenomenologically determined 16O + 16O and 16O-n potentials reproduces the measured cross sections within the limitations of the model. A possible error in the data analysis for 16O + 17O by Thomas et al. is pointed out.