The stability of two vortex pairs is analysed as a model for the vortex system generatedby an aircraft in flaps-down configuration. The co-rotating vortices on the starboard andport sides tumble about one another as they propagate downward. This results in atime-periodic basic state for the stability analysis. The dynamics and instability of thetrailing vortices are modelled using thin vortex filaments. Stability equations are derivedby matching the induced velocities from Biot–Savart integrals with kinematic equationsobtained by temporal differentiation of the vortex position vectors. The stability equationsare solved analytically as an eigenvalue problem, using Floquet theory, and numerically asan initial value problem. The instabilities are periodic along the axes of the vortices withwavelengths that are large compared to the size of the vortex cores. The results showsymmetric instabilities that are linked to the long-wavelength Crow instability. Inaddition, new symmetric and antisymmetric instabilities are observed at shorter wavelengths.These instabilities have growth rates 60–100% greater than the Crow instability. The systemof two vortex pairs also exhibits transient growth which can lead to growth factors of 10 or15 in one-fifth of the time required for the same growth due to instability.