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In this paper, a new fairness notion is proposed for languages with multi-party interactions as the sole interprocess synchronization and communication primitive. The main advantage of this fairness notion is the elimination of starvation occurring solely due to race conditions (i.e., ordering of independent actions). Also, this is the first fairness notion for such languages which is fully adequate with respect to the criteria presented in [2]. The paper defines the notion, proves its properties, and presents examples of its usefulness.