The nonvanishing elements of the viscosity and thermal conductivity tensors of polyatomic gases fall into two classes: those that change sign with a rotation about the magnetic field line and those that do not. It is shown that the boundedness of the linearized Waldmann-Snider collision operator and its properties under symmetry transformations imply that for linear Zeeman splitting the first class vanishes at zero and infinite field as ¦ B ¦ and ¦ B ¦-1 and that the second class approaches its asymptotes as ¦ B ¦2 and ¦ B ¦-2.