For several years, the BNM-Laboratoire Primaire du Temps et des Frequences has worked on a cold atom frequency standard. With a cesium atomic fountain a resonance line width of 700 mHz has been obtained leading to a short-term stability of 2 10 - 1 3 τ - 1 2 down to 2 10 - 1 5 at 10 4 s. A first evaluation of the fountain accuracy has been performed resulting in an accuracy of 3 10 - 1 5 , three times better than previously achieved with thermal beams frequency standards. In the atomic fountain, gravity limits the interaction time to 1 s, hence the resonance line width to 0.5 Hz. A factor of 10 reduction in the line width could be obtained in a micro-gravity environment. The Centre National d'Etudes Spatiales (the French space agency), the BNM-Laboratoire Primaire du Temps et des Frequences , the Laboratoire de l'Horloge Atomique and the Laboratoire Kastler Brossel have set up a collaboration to investigate a space frequency standard using cold atoms: the PHARAO project. A microgravity prototype has been constructed and operated first in the reduced gravity of aircraft parabolic flights in May 1997. It is designed as a transportable frequency standard. The PHARAO frequency standard could be a key element in future space missions in fundamental physics such as SORT (solar orbit relativity test), detection of gravitational waves, or for the realization of a global time scale and a new generation of positioning system.