Momentum-transfer theory has been used to obtain a relationship between the nth order tensorial transport coefficients in a swarm experiment, the (n - 1) th derivative of the mobility, and the nth derivative of the reaction rate coefficient. Elastic, inelastic, and reactive collisions for gas mixtures have been taken into consideration. Numerical comparisons show that the results obtained from this relationship are in good agreement with those obtained by solution of the Boltzmann equation. Finally, we have analyzed the structure of the third-order tensorial transport coefficient by applying momentum-transfer theory and group theory; both approaches show that in general there are three independent components of this rank-three tensor.