This paper gives an overview of the French national project on automatic speech processing ("GRECO on Speech Communication") funded by CNRS and the Ministry of Research and Technology. We will first concentrate on the role and objectives of the project and then present the six domains which are presently investigated database of spoken French, database of morphological and lexical aspects of spoken French, acoustic-phonetic decoding of speech, design of a workstation for speech research and development, man-machine dialog using speech, use of prosody in speech recognition.