In the present work, slow atomic collisions with changes of atomic spins are examined. In this case, the electron spin exchange in the process of collisions causes the polarization characteristics of atoms to change. Formalism has been constructed based on the adiabatic approximation and polarization operator technique for a description of changes of arbitrary spins of colliding atoms. Singlet-triplet transitions, analogous to those of inelastic exchange electron scattering on two-electron atoms, are described for collisions of hydrogen and alkali metal (H, K, Na, Cs, and Rb) atoms with two-electron atoms or ions (He, Li + , and Hg). The processes of the type 2 1 2 3 H( ) He( ) H( ) He( ) S S S S