Among the collection of projects which emerged from Miles during World War 2, two of the strangest were the Miles M.35 and M.39 tandem-wing aircraft, and while most of the projects did not materialize these two were built and flown.

The following are some of the advantages claimed regarding the design. Both wings contribute to the total lift, and the parasitic drag, weight and download of a tailplane is eliminated; span and length dimensions are less than those of a comparable orthodox aeroplane, making for constructional strength at less weight and increased manœuvrability; the pilot's field of vision is greatly improved, while the general plan of the aircraft lends itself to the popular tricycle undercarriage. A further advantage of the Libellula layout is that, since the two lifting surfaces are disposed on either side of the centre of gravity, the large change in trim normally encountered by the use of high lift devices can be balanced out, while the permissible range of movement for the centre of gravity can be extended to a degree quite unattainable on either an orthodox, a tail-first or a tailless machine.

At the end of 1941 the M.35 was conceived of using the tandem-wing arrangement, with the pilot being in the extreme nose with the pusher engine mounted behind the rear wing, in the design of a carrier-borne naval fighter. The advantages of such a form being the reduced hangar space required - the short wing span meant that wing-folding was not needed and therefore simplified ship-board handling, and the perfection of view obtainable for the landing-on approach.
Such was the enthusiasm for the project that a rough flying scale mock-up was designed, built and flown in only six weeks, the first flight being made by Mr. G. H. Miles early in 1942. Slight longitudinal stability deficiencies became apparent during extended trials, but wind tunnel tests showed the problems to be curable and George Miles conceived a heavy bomber, the M.39, to be powered by three turbojet engines, or in its initial form with two high-altitude Rolls-Royce Merlin 60s or Bristol Hercules VIIIs.
A 5/8 scale model of the bomber was built and designated M.39B, flying for the first time on 22nd July 1943 and proving to be aerodynamically stable. Flight trials were initially on a private basis, but in 1944 the M.39B went to the Royal Aircraft Establishment at Farnborough, where it suffered two accidents. After extensive repairs the work ended and the aircraft was broken up
The whole Miles tandem-wing range of aircraft was given the class name of Libellula, which is the entomological title of members of the dragon-fly insect family.