  Let c be an integer. A c-partite tournament is an orientation of a complete
c-partite graph. A c-partite tournament is rich if it is strong, and each
partite set has at least two vertices. In 1996, Guo and Volkmann characterized
the structure of all rich c-partite tournaments without (c + 1)-cycles, which
solved a problem by Bondy. They also put forward a problem that what the
structure of rich c-partite tournaments without (c + k)-cycles for some k>1 is.
In this paper, we answer the question of Guo and Volkmann for k = 2.
