Motion equations describing streams of relativistic particles and their
properties are explored in detail in the framework of Cosmological Perturbation
Theory. Those equations, derived in any metric both in the linear and nonlinear
regimes, express the matter and momentum conservation. In this context we
extend the setup of adiabatic initial conditions - that was initially performed
in the Conformal Newtonian gauge - to the Synchronous gauge. The subhorizon
limit of the nonlinear motion equations written in a generic perturbed
Friedmann-Lema\^{i}tre metric is then derived and analyzed. We show in
particular that the momentum field Pi(x) is always potential in the linear
regime and remains so at subhorizon scales in the nonlinear regime. Finally the
equivalence principle is exploited to highlight invariance properties satisfied
by such a system of equations, extending that known for streams of
non-relativistic particles, namely the extended Galilean invariance
