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 Ѓ B Ѓ and Ѓ B Ѓ-1 and that the second class approaches its asymptotes as Ѓ B Ѓ2 and Ѓ B Ѓ-2.