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The recently proposed pair-exchange diffusion model for multicomponent diffusion in a random alloy is analyzed in detail. The model defines the differences of chemical potential gradients of two elements as general driving forces for interdiffusion and the corresponding proportionality coefficients as pair-mobilities for atomic exchange fluxes of a pair of elements at the mesoscopic scale. The total fluxes of alloying elements are given as the sum over corresponding pair-contributions, which rely on a set of independent forces and maintain a meaningful symmetric form to satisfy Onsagers reciprocal relations. It is demonstrated that a consistent definition of interdiffusion coefficients requires the fulfillment of the Gibbs-Duhem relation by the applied thermodynamic Gibbs energy description. The expression for the marker velocity for multicomponent random alloy is derived in the pair-wise form as a sum of the differences of chemical potential gradients of two elements with the linear coefficients which are differences between corresponding mobilities. The application of the model to High Entropy Alloys is demonstrated.