The causal order in distributed asynchronous systems is a valuable and useful concept to implement distributed algorithms. In particular, causal broadcasts have been used to solve-many well-known distributed problems (as replication using a token-passing mechanism), ttowever, the implementation of a general causal message system (where every message and broadcast respects the causal order) is complicated and involves a hard protocol to ensure delivery order. Ou the other hand only a few applications really need the causal semantics of the message sending primitives and they typically only concern the broadcast primitives.This paper proposes a new ordering of broadcasts and messages, where the broadcasts are causally ordered, but they only impose an order on messages (which are not causally ordered). This order (called large causality) is easy and cheap to implement on most distributed architectures and is powerful enough to build token-passing (and though replica coherency) and global state applications.This paper does not treat group multicast nor fault-tolerance, however we expect to be able to benefit from the research done on this field by systems such as ISIS, providing all these features together.