Formulas are developed to describe the rotational energy of a linear polyatomic molecule in a 2Σ or 3Σ electronic state, where one or more quanta of a degenerate bending vibration are excited. In 2Σ states the spin doubling and l-type doubling are independent, provided that the rotational constant B is large compared with the spin–rotation interaction constant γ. In 3Σ states the normal triplet splitting patterns (e.g. Schlapp's formulas) are considerably altered by the presence of vibrational angular momentum at low rotational quantum number N, especially when the spin–spin interaction parameter λ is sizeable; however, with increasing rotation, the normal spin and l-type doubling patterns are approached, as the vibrational angular momentum is progressively uncoupled from the molecular axis.