When you say "they stay on" are they very dim?
If so, then it is capacitive effects, caused by 2-way switching - long runs of wires side by side leak electrons to each other, the longer the wire, the bigger the effect. Between the 2 switches controlling the landing lights, is the place this becomes most apparent.
When you put a halogen in the circuit, the electrons have an easier path to neutral, through its filament, so the LEDs (through which the electrons would have to pass a semiconductor) stay dead.
With energy saving lamps (the usual type), they exhibit this capacitive effect by flickering gently every few seconds.
IMO its nothing to worry about, but it does worry some people. LEDs use so little power anyway.