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We propose a simple method for determining the redshift $z_{m}$ at which the angular size of an extragalactic source with fixed proper diameter takes its minimal value. A closed analytical expression, which is often convenient for numerical evaluation is derived. The method is exemplified with the following FRW type expanding universes: the open matter dominated models ($\Omega_{\Lambda} = 0$), a critical density model with cosmological constant ($\Omega_{\Lambda} \neq 0$), and the class of scalar field cosmologies proposed by Ratra and Peebles. The influence of systematic evolutionary effects is briefly discussed

LETTER: On the Minimal Angular Size in Open, ΛCDM, and Scalar Field Cosmologies