The problem of complementary cycles in tournaments and bipartite tournaments was completely solved. However, the problem of complementary cycles in semicomplete *n*-partite digraphs with *n* ≥ 3 is still open. Based on the definition of componentwise complementary cycles, we get the following result. Let *D* be a 2-strong n-partite (*n* ≥ 6) tournament that is not a tournament. Let *C* be a 3-cycle of *D* and *D* \ *V* (*C*) be nonstrong. For the unique acyclic sequence *D*_{1},*D*_{2}, ...,*D*_{α} of *D**V* (*C*), where *α* ≥ 2, let *D*_{c} = {*D*_{i}\*D*_{i} contains cycles, *i* = 1, 2, ..., α},
$$D_{\bar c} = \{ D_1 ,D_2 , \cdots ,D_\alpha \} \backslash D_c$$
. If *D*_{c} ≠ ∅, then *D* contains a pair of componentwise complementary cycles.