A method of determining the longitudinal air speed V.sub.airX and the longitudinal ground speed V.sub.solX of a rotary wing aircraft depending on the exposure of the aircraft to the wind, the aircraft flying at a speed of advance Va. The method making it possible to determine characteristic speed curves for the aircraft depending on the longitudinal speed of the relative wind to which the aircraft is subjected, and then during a flight and depending on the actions of the pilot of the aircraft, to deduce the longitudinal ground speed V.sub.solX and the longitudinal air speed V.sub.airX to be applied to the aircraft depending on variations in the longitudinal speed of the relative wind to which the aircraft is subjected.