Unstable recycling systems containing delay terms pose a challenge problem in their own. When unstable time delay system have recycle the control problem becomes even more difficult. In this work it is proposed a control methodology for the stabilization and control of recycling systems with one unstable and m stable poles in the direct path and a delayed stable subsystem in the backward loop. The strategy is based on the observation that if some internal signals were available, then it would be possible to decouple the backward dynamics and then a feedback controller could be designed for the forward dynamics. The key for this strategy to be carried out is the asymptotic observer-predictor proposed to estimate the required internal signals. Necessary and sufficient conditions are stated in order to guarantee the stabilization of the proposed scheme, achieving step tracking and step disturbance rejection. Then, the strategy is extended to a more general family of plants including " p " left half plane zeros (LHP) in the direct path.