Define anycast services as a group of replicated servers that may provide similar or identical services. Using anycast services can significantly simplify some applications such as to seek appropriate servers to provide quality of service and to achieve the load balance and fault-tolerance for service availability. An anycast flow is a sequence of packet that can be established between a user and any server in an anycast (replicated) service group. This paper studies a set of efficient distributed connection setup algorithms for real-time anycast flows. Given an anycast flow between a server j and a request node s with end-to-end deadline D_s,j and minimum bandwidth requirement B_s,j, our algorithms can effectively seek multiple destination connections in parallel thus the best path which satisfies the requirements of the anycast flow is chosen. The deterministic approach for worst delay bound analysis is also given.