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A general algorithm to construct particle trajectories in 1+1 dimensionalcanonical relativistic models is presented. The method is a generalization ofthe construction used in Ruijsenaars-Schneider models and provides a simpleproof of the fact that the latter satisfies the world-line conditions grantingproper physical Poincare invariance. The 2-particle case for the rationalRuijsenaars-Schneider model is worked out explicitly. It is shown that theparticle coordinates do not Poisson commute, as required by the no-interactiontheorem of Currie, Jordan and Sudarshan.

Relativistic trajectory variables in 1+1 dimensional Ruijsenaars-Schneider type models