This thesis mainly deals with the existence of directed cycles and directed paths (or short: cycles and paths, respectively) with certain properties in close to regular multipartite tournaments. A multipartite tournament is an orientation of a complete multipartite graph. The statements in this thesis depend on how much a multipartite tournament differs from being regular. Chapters 2 to 4 consist of several results about cycles in multipartite tournaments: short cycles of a given length containing a given arc, cycles through a given arc and a given number of partite sets and cycles with a given number of vertices from each partite set. In Chapter 5 a bound of Yeo about the connectivity in close to regular multipartite tournaments is studied. Furthermore, in the last 3 chapters we look for paths in multipartite tournaments: paths containing a given number of vertices from each partite set, Hamiltonian paths and Hamiltonian paths containing a given arc
