Collision cross sections and rate constants between two ground- state oxygen molecules are investigated theoretically at translational energies below ∼ 1K and in zero magnetic field. We present calculations for elastic and spin- changing inelastic collision rates for different isotopic combinations of oxygen atoms as a prelude to understanding their collisional stability in ultracold magnetic traps. A numerical analysis has been made in the framework of a rigid- rotor model that accounts fully

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... or the singlet, triplet, and quintet potential energy surfaces in this system. The results offer insights into the effectiveness of evaporative cooling and the properties of molecular Bose- Einstein condensates, as well as estimates of collisional lifetimes in magnetic traps. Specifically, ^17O_2 looks like a good candidate for ultracold studies, while ^16O_2 is unlikely to survive evaporative cooling. Since ^17O_2 is representative of a wide class of molecules that are paramagnetic in their ground state we conclude that many molecules can be successfully magnetically trapped at ultralow temperatures.