Earlier theoretical and computer studies on the dynamics of strongly coupled charged particle bilayers have revealed the existence of an energy gap (ω(k 0) ≠ 0, optical behaviour) for the out-of-phase plasmon. This is in contrast to the correlationless RPA prediction of acoustic (ω ∼ k) behaviour. We have studied the question whether a classical perturbation calculation for weak coupling shows the onset of the energy gap, and whether there is a minimal coupling threshold for the formation of the gap. A formally exact lowest order expansion technique due to Zhang and Kalman (1992 Phys. Rev. A 45 5935) has been used.