  We calculate analytically and numerically the Dyer-Roeder distance in perfect
fluid quintessence models and give an accurate fit to the numerical solutions
for all the values of the density parameter and the quintessence equation of
state. Then we apply our solutions to the estimation of $H_{0}$ from multiple
image time delays and find that the inclusion of quintessence modifies sensibly
the likelihood distribution of $H_{0}$, generally reducing the best estimate
with respect to a pure cosmological constant. Marginalizing over the other
parameters ($\Omega_{m}$ and the quintessence equation of state), we obtain
$H_{0}=71\pm 6$ km/sec/Mpc for an empty beam and $H_{0}=64\pm 4$ km/sec/Mpc for
a filled beam. We also discuss the future prospects for distinguishing
quintessence from a cosmological constant with time delays.
