I will present a new set of equations, designed to study the time evolution of relativistic species in the nonlinear regime. Derivation is based on conservation laws. In this approach, the standard study of a phase-space distribution function is replaced by a study of two macroscopic fields per flow. Focusing on subhorizon scales, all the physical information is eventually encoded in a compact and handy motion equation. Any free-streaming species, relativistic or not, can be included in it. Invariance properties of the different equations will also be discussed.