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Microwave H2, N2, and N2-Ar discharges driven by traveling surface waves are investigated as sources of ground state N(4S), H(1s) atoms. The dissociation kinetics is discussed in the framework of theoretical models based on a self-consistent treatment of the main discharge balances, wave electrodynamics and plasma-wall interactions. It is shown that the number density of hydrogen H(1s) atoms depends heavily on the wall conditions at low pressure conditions. The kinetics of N(4S) and metastable N(2D) and N(2P) atoms and of the molecular N2(A3Σu+) metastable state in a pure N2 discharge are shown to be strongly coupled. One possible way to control and to enhance nitrogen dissociation is the use of an N2-Ar mixture. The increase in dissociation degree of N2 molecules at high Ar fractional concentration can be attributed to dissociative recombination between electrons and N2+ positive ions. The predicted results for the atomic density are compared with emission spectroscopy data.