  We study the efficiency of numerically simulated galaxy clusters for
producing strong gravitational lensing events in different dark-energy
cosmologies with constant and time-variable equation of state and we compare it
with ``standard'' $\Lambda$CDM and OCDM models. Our main results are that: (1)
the expected abundance of gravitational arcs with large length-to-width ratio
depends on the equation of state of dark energy at the epoch of formation of
the halo; (2) as found in previous studies, the strong lensing cross section of
galaxy clusters is very sensitive to dynamical processes like mergers, whose
impact however is different for different cosmologies, being stronger for
models in which halos are less concentrated. As expected, the largest
differences in the lensing optical depth occur at moderate and high redshift.
