To successfully develop certain competences in students, it is necessary to define the competences, as well as to set assessment criteria to be used in the process of developing, assessing and further developing of the competences. Due to the developing nature of international cooperation among organizations, the criteria for assessing international cooperation competences must comprise and assess all components of the particular competences that are necessary in typical job situations in the present time in the field where the prospective specialists (the current students) are planning to work, as well as all components of competences that individuals should possess in accordance with the constructivist learning theory, thus fostering a learning environment where students motivate themselves and construct their knowledge accordingly. The article defines international cooperation competences of external relations specialists, as well as sets, describes and justifies their assessment criteria, taking into account the prospective job environments of these specialists along with progressive learning theories. The set assessment criteria can also be used to assess international cooperation competences of students of other study fields where foreign language or communication courses are acquired. Apart from defining international cooperation competences and their assessment criteria, the study results present the comparison of the assessment of competences by means of using the set criteria and grades in simulations and in the standard written final examination, thus justifying the need for the set criteria to assess the most important components of the mentioned competences properly on the basis of practical competence demonstration and testing.