  An almost-stationary gauge condition is proposed with a view to Numerical
Relativity applications. The time lines are defined as the integral curves of
the timelike solutions of the harmonic almost-Killing equation. This vector
equation is derived by a variational principle, by minimizing the deviations
from isometry. The corresponding almost-stationary gauge condition allows one
to put the field equations in hyperbolic form, both in the free-evolution ADM
and in the Z4 formalisms.
