Event ordering is an important research subject in Distributed Systems (DS). Event ordering addresses the problem of establishing a certain order among the events that occur in DS according to some particular criteria. The types of event orderings used for DS are no order, FIFO, causal, Δ-causal, total and causal-total. They mainly differ in the degree of asynchronous execution allowed. One of the most important orderings is the Causal Order (CO), which is based on Lamport’s happened-before relation. It establishes that the events must be seen in the cause-effect order as they occur in the system. However, for certain applications, for example multimedia synchronization, where some degradation of the system is allowed, ensuring the CO based on Lamport’s relation is rigid and negative affect the performance of the system. In this study, it is introduced a new ordering for DS in order to achieve a more asynchronous execution than the CO, this new ordering is called Fuzzy Causal Order (FCO). Besides, it is defined the Fuzzy Causal Relation (FCR) and Fuzzy Causal Consistency (FCC), the FCR establishes logical dependencies based on the precedence of events and by considering some kind of distance between their occurrences. With the notion of distance was possible to establish a cause-effect measure between two events a and b that indicates how long ago an event a happened before an event b. Through the FCC it was possible to determine how good the performance of the system is at a given moment. The usefulness of the FCO, FCR and FCC is showed by applying them to the concrete problem of intermedia synchronization in DS.