  Given a path of almost-K\"ahler metrics compatible with a fixed symplectic
form on a compact 4-manifold such that at time zero the almost-K\"ahler metric
is an extremal K\"ahler one, we prove, for a short time and under a certain
hypothesis, the existence of a smooth family of extremal almost-K\"ahler
metrics compatible with the same symplectic form, such that at each time the
induced almost-complex structure is diffeomorphic to the one induced by the
path.
