Free flights of a damselfly, Ceriagrion melanurum Selys, are filmed with a high speed video camera and analyzed on a personal computer based image processing system. The observed characteristics of the flight are : 1) The flight speed is rather low. lt ranges from 0.4m/s to 0.9m/s in our experiments. 2) The inclinations of the stroke planes are small. It is 10~15 deg for the forewing and 0~30 deg for the hindwing. 3) The flapping amplitude of the wing is almost twice as large as that of a dragonfly for the fore and hindwing respectively. 4) The phase difference between fore and hind pairs of wings is about -100 deg. lt is 60~90 deg in the flight of a dragonfly. We use the Fourier analysis to make clear the beating mechanism of wings ; the flapping motion can be expressed by the first harmonic of a Fourier expansion series, while the higher harmonics were needed to simulate the feathering motion of the wing