Stateful aspects is a recent topic in AOSD. As the trigger of a stateful aspect depends on the system execution trace, it needs complicate modeling mechanisms for the pointcuts and weaving operations. We present an approach to weaving stateful aspects using Labelled Transition System (LTS). In the approach, the base system is specified as a LTS. The pointcut is modeled as an extended LTS that observes the trace of the base system and decides the activation points for the advices. The composition of the pointcut and the base system can achieve a LTS that is semantically consistent with the base system. The advice weaving is modeled as transformation operations on the composition of the base system and the pointcut. These weaving operators can preserve the semantic equivalence between systems. The approach has been implemented on a FSP based prototype tool.