An attempt is made to show that it is possible to constnuct a theory of particle systems in accord with the basic ideas of the causal interpretation of wave mechanics by the theory of the double solution. After a discussion of the theory of the individual particle, the de Broglie and Vigier theories on the causal interpretation of the theory of systems are examined. It is then shown that it is possible to reframe the analytical mechanics of systems and, in particular, the Hamilton-Jacobi theory in a space with three dimensions. The question of the form of the basic equations in physical space is discussed in detail. The statistical theory of systems of particles of different nature is explained. (J.S.R.)