  We investigate the influence of an exotic fluid component ("quintessence") on
the angular size-redshift relation for distant extragalactic sources.
Particular emphasis is given for the redshif $z_{m}$ at which the angular size
takes its minimal value. We derive an analytical closed form which determines
how $z_m$ depends on the parameter of the equation of state describing the
exotic component. The results for a flat model dominated by a "quintessence"
are compared in detail with the ones for the standard open model dominated by
cold dark matter. Some consequences of systematic evolutionary effects on the
values of $z_{m}$ are also briefly discussed. It is argued that the critical
redshift, for all practical purposes, may completely be removed if such effects
are taken into account.
