The H-theorem in μ-space for a mixture of free molecules or particles A, B, ... undergoing all sorts of multiple collisions or reactions (creation and annihilation) is generalized to the case, where detailed balancing (DB) does not hold, and for the 3 statistics (Boltzmann, Bose-Einstein, and Fermi-Dirac). The equilibrium condition is given in terms of the chemical potentials μ_A, μ_B, ... The transition probabilities between macrocells have to satisfy a weaker condition than DB.