Abstract In this paper we consider whether a system of gravitational masses radiates energy. First we try to define gravitational radiation in a simple way. Its total flux equals the time derivative of the gravitational linear momentum. Then the principal question arises whether or not this gravitational linear momentum is constant. This question, when properly formulated, is intimately connected with the problem of the motion of particles in their gravitational field. We trace this connection and return ultimately to our principal question. The answer is: we can always find a reasonable coordinate system in which there is no gravitational radiation.