Nonlinear irreversible processes between states which are not local equilibrium states are investigated by methods of the kinetic theory. The phenomenological equations for the second-order fluxes in a multicomponent mixture are derived, and relations between some of the second-order phenomenological coefficients are established. It is shown that new independent forces appear in the second-order equation, namely the gradients of the chemical potentials. Expressions for the entropy, entropy flux, and entropy source are evaluated. These expressions are related to the phenomenological equations and coefficients, e.g., all the second-order contributions of the forces in the equations for the fluxes can be obtained by differentiation of the expression for the second-order entropy source with respect to the coupled forces.