Two families of matrices play an important role in the analysis of Markov additive processes (MAPs). The first one is related to first passage times from one level to another and was the subject of Chap. 2 . The second family is about the expected time spent byMarkov additive process the MAP in various locations between successive visits to its initial level; it is the object of the present chapter, and we show in a next chapter that it is fundamental in expressing the stationary distribution of regulated processes. Firstly, we the local time spent by the process at a given level; we give some of its basic properties. Next, we introduce the matrix R such that \(e^{R x}\) is the expected local time spent at level x per unit of local time spent at level 0. We analyse the connection between R and the matrix U from Chap. 2 , both when \(\boldsymbol \pi ^{\mathrm {T}} \boldsymbol \mu \neq 0\) and when \(\boldsymbol \pi ^{\mathrm {T}} \boldsymbol \mu =0\) . In closing the chapter, we prove the relation between the matrices R and U of the given MMBM and those of the time-reversed process.