Collisions between slow atomic particles involving a small change in electron energy in the transition are examined. Asymptotic methods are presented for calculating the parameters of interaction potentials for atomic particles at large separations. Different models describing electron transitions during collisions between atomic particles are analyzed. The simultaneous use of the asymptotic method for the calculation of the interaction potentials between colliding particles and of the generalized two-level approximation for the quasiresonant particle collision results in reliable calculations of transition cross sections for a broad range of processes. This is demonstrated by considering examples of resonant charge transfer, spin exchange, and also some quasiresonant processes.