Instabilities associated with streamlines connecting stagnation points in an equilibrium with plane incompressible flow are studied. It is shown that they belong to two different types: If the velocity of fluid absorption at the endpoint is greater than the velocity of fluid emission at the initial point, only a discrete spectrum of unstable standing waves is possible; otherwise, Alfvénic waves accumulate to form a continuum of unstable frequencies. These are present no matter how small the equilibrium field or the mode number of the magnetic oscillations.