´Eventual´ is earlier than ´immediate´

Two different notions of Byzantine Agreement - immediate and eventually - are defined depending on whether the agreement involves an action to be performed synchronously or not. The lower bounds for time complexity depend on what kind of agreement has to be achieved. All previous algorithms to reach Byzantine Agreement ensure immediate agreement. We present two algorithms that in many cases reach the second type of agreement faster than previously known algorithms showing that there actually is a difference between the two notions: Eventual Byzantine Agreement can be reached earlier than Immediate.