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Coriolis forces break the infinite-fold axis of symmetry of a linear molecule, but leave a residual plane of symmetry. Thus the rovibronic (or spin.rovibronic) wavefunctions can be classified according to their behavior under reflection of the vibronic (or spin.vibronic) variables in this plane. The orientation of the plane depends on the coupling case. In Hund's case (a) or (e) the plane is through the molecular axis normal to the perpendicular component of the angular momentum J, while in Hund's case (b) it is normal to the perpendicular component of N. The former gives an exact symmetry classification equivalent to the $e/f$ classification of Ref. 1, while the latter gives an approximate symmetry classification equivalent to the $A\prime /A\prime \prime$ classification proposed in Ref. 2. A simple prescription for the latter notation is given, namely $A\prime levelshaveparity+(-1)NA\prime \prime levelshaveparity-(-1)N$ This gives a useful characterization even when N is not a perfect quantum number. The classification of case (d) rovibronic levels in terms of the symmetries of the levels of the core will also be considered briefly.