The object of this paper is to uncover the nature of the destabilising coupling that is the major cause of body-freedom flutter and to see whether a simple cure for the flutter can be found. To do this frequency-coalesence theory is applied to a simple aircraft. It is shown that the aircraft is liable to flutter if it has a sweptforward wing and a positive ‘tail-off’ cg margin or a sweptback wing and a negative cg margin but a simple cure for the flutter does not appear to exist.