Normality, consitancy criteria stronger than sequentiality and equivalant to linearizability for the unary operations case, has the main advantage that it avoids the use of the "global real-time ordering". This work presents the first algorithm that implements normality without using strong communication primitives (i.e. atomic broadcast or global clock syncronization). Moreover, our implementation allows the dynamic changes of the system configuration, handles replication and refers the general case of multi-object operations. Although the use of terms as client or server our algorithm is entirely based on a peer-to-peer approach.