In distributed modeling and simulation area, it is intractable to comprehend the fundamental principles of optimistic advancing mechanism and implement the optimistic advancing services in RTI (runtime infrastructure) according to HLA (high level architecture) specifications. This paper introduces two different optimistic advancing mechanisms in PDES (parallel discrete event simulation) and HLA, and reveals some important differences between them. For example, the virtual time can be rolled back in PDES, the logical time can not be rolled back in HLA, and an optimistic federate can only roll back its message-scheduling time and must ensure that its rollback won’t influence the advancing of conservative federates. Rollback occurs in a logical process in PDES, but it can only occur in a federate rather than RTI in HLA. In addition, a new implementation mechanism called Zero-Saving is proposed in this paper. With this mechanism, a RTI does not need to save any execution states when optimistic advancing services are implemented. This mechanism has successfully been applied to a RTI named StarLink. The Zero-Saving mechanism adds two new variables into the message retraction handle type RTI::MessageRetraction Handle which is a data type defined by IEEE 1516.1. One variable represents the time stamp of the sent TSO (time stamp order) message, and the other is used to save all federates which receive the message. When a TSO message is sent to RTI, RTI returns the sending federate a message retraction handle with all message-received federates. So RTI knows which federates should be notified to retract the received messages whenever the sending federate uses a message retraction handle to ask RTI to retract a TSO message. The fundamental principles and implementation of optimistic advancing services introduced in this paper are useful for RTI developers.