Subject of study. Magnetic resonance frequency shifts caused by spin exchange collisions involving optically oriented alkali atoms in the ground state are studied. Aim of study. Spin-exchange collisions involving optically oriented pairs of alkali atoms of different types are theoretically studied to determine the shifts in the magnetic resonance line frequencies as a function of temperature for various pairs of alkali atoms under various optical orientation conditions in order to determine optimum constraints for the construction of quantum magnetometers with optical pumping using mixtures of alkali atoms. Method. Collisions between optically oriented alkali atoms are analyzed within the framework of quantum scattering theory, and data on the interaction potentials of alkali-atom dimers are used to calculate the scattering phases for collisions involving these potentials and the imaginary parts of the complex spin-exchange cross-section. The resulting cross sections as a function of energy were used to determine the magnetic resonance frequency shifts as a function of temperature. Main results. The magnetic resonance line frequency shifts for the following pairs of alkali atoms were obtained as a function of temperature: 39K−133Cs, 39K−85Rb, and 133Cs−85Rb. The shift in the magnetic resonance line involving the F=1 hyperfine state for a 39K−85Rb alkali-atom pair was found to pass through zero near temperature 480 K. Practical significance. The results obtained in this paper can be used to develop zero-spin-exchange-shift quantum electronic devices based on the optical orientation of atoms. In particular, it is possible to develop co-magnetometers based on the optical orientation of alkali atoms.