Angular size in quintessence cosmology

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.