Reactive Fiffo Systems (RFS) are used to model reactive systems which are able to memorize the events that cannot be processed when they occur. In this paper we investigate the decidability of verification problems for Embedded RFS which are RFS running under some environmental constraints. We show that almost all the usual verification problems are undecidable for the class of Periodically Embedded RFS with two memorizing events, whereas they become decidable for Regularly Embedded RFS with a single memorizing event. We then focus on Embedded Lossy RFS and we show in particular that for Regularly Embedded Lossy RFS the set of predecessors Pred* is upward closed and effectively computable.