This paper proposes the first implementation of a regular register by n servers that is tolerant to both mobile Byzantine agents, and transient failures (it is self-stabilizing) in a round-free synchronous model. We consider the most difficult model for mobile Byzantine agents to date where the message delay, δ, and the speed of mobile Byzantine agents, ∆, are completely decoupled. Moreover, servers are not aware of their state (infected or correct) after mobile Byzantine agents left them. The register is maintained by n servers and our algorithm tolerates (i) any number of transient failures , and (ii) up to f Mobile Byzantine agents. Our implementation uses bounded timestamps from the Z 5 domain, and is optimal with respect to the number of tolerated mobile Byzantine agents. The convergence time of our solution is upper bounded by 3∆ + T_5write() , where T_5write() is the time needed to execute five complete write() operations.