The cross sections of arbitrary-shaped non-paraxial light beams are ch
aracterized by the zero, first and second order moments of the energy
flux spatial distribution. On the basis of the Maxwell equations and a
plane wave spectrum representation of electromagnetic fields, the law
s governing the change of these moments upon free beam propagation are
found. In particular, the change of the second-moment-based width is
found to be hyperbolic. The moment-based parameters are calculated and
the hyperbolic law applied to some particular non-paraxial beam-like
electromagnetic field models to show some new features that arise from
this non-paraxial vectorial theory.