Two sets of rate coefficients for low-energy inelastic potassium-hydrogen and rubidiumhydrogen collisions were computed for each collisional system based on two model electronic structure calculations, performed by the quantum asymptotic semi-empirical and the quantum asymptotic linear combinations of atomic orbitals (LCAO) approaches, followed by quantum multichannel calculations for the non-adiabatic nuclear dynamics. The rate coefficients for the charge transfer (mutual neutralization, ion-pair formation), excitation and de-excitation processes are calculated for all transitions between the five lowest lying covalent states and the ionic states for each collisional system for the temperature range 1000-10 000 K. The processes involving higher lying states have extremely low rate coefficients and, hence, are neglected. The two model calculations both single out the same partial processes as having large and moderate rate coefficients. The largest rate coefficients correspond to the mutual neutralization processes into the K(5s 2 S) and Rb(4d 2 D) final states and at temperature 6000 K have values exceeding 3 × 10 −8 cm 3 s −1 and 4 × 10 −8 cm 3 s −1 , respectively. It is shown that both the semi-empirical and the LCAO approaches perform equally well on average and that both sets of atomic data have roughly the same accuracy. The processes with large and moderate rate coefficients are likely to be important for non-LTE modelling in atmospheres of F, G and K-stars, especially metal-poor stars.