  We study finite and countably infinite systems of stochastic differential
equations, in which the drift and diffusion coefficients of each component
(particle) are determined by its rank in the vector of all components of the
solution. We show that strong existence and uniqueness hold until the first
time three particles collide. Motivated by this result, we improve
significantly the existing conditions for the absence of such triple collisions
in the case of finite-dimensional systems, and provide the first condition of
this type for systems with a countable infinity of particles.
