  We propose a generalisation of the local causality principle of space-time,
asserting that it holds for all regimes of motion, including superluminal
motions. It assumes the existence of a countably infinite set of metrical null
cone speeds, $c_k$, where the first one, $c_1=c$, corresponds to the speed of
light in vacuum. Our associated space-time measures do not diverge at the
maximum speed of each interval of speeds and implies a generalisation of
Einstein's rule for velocities addition. We construct a causal structure for
each regime of motion. After introducing a simple dynamical measure, we derive
an expression for the energy of material particles, which approaches the
relativistic one when $v<c$. An experiment to energise photons in an 1-1
process is proposed as a test of our interpretation of the non divergence at
the speed of light of present space-time measures. We discuss also the possible
transition of a material particle from the subluminal regime $v<c$ to the first
superluminal regime and vice versa, making discrete changes in $v^2/c^2$ around
the unit in terms of a very tiny constant, $\epsilon^2$, which we introduce to
prevent the divergence of the Lorentz $\gamma$ factor at the speed of light in
vacuum.
