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We consider communication structures for event ordering algorithms in distributed environments where information flows only in one direction. Example applications are multilevel security and hierarchically decomposed databases. Although the most general one directional communication structure is a partial order, partial orders do not enjoy the property of being consistently ordered, a formalization of the notion that local ordering decisions are ensured to be globally consistent. Our main result is that the crown free property is necessary and sufficient for a communication structure to be consistently ordered. We discuss the computational complexity of detecting crowns and sketch typical applications.