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Competition graphs were created in connected to a biological model as a meansof reflecting the competition relations among the predators in the food websand determining the smallest dimension of ecological phase space. In 2011,Factor and Merz introduced the (1,2)-step competition graph of a digraph. Givena digraph $D=(V,A)$, the (1,2)-step competition graph of $D$, denoted$C_{1,2}(D)$, is a graph on $V(D)$ where $xy\in E(C_{1,2}(D))$ if and only ifthere exists a vertex $z\neq x,y$ such that either $d_{D-y}(x,z)=1$ and$d_{D-x}(y,z)\leq 2$ or $d_{D-x}(y,z)=1$ and $d_{D-y}(x,z)\leq 2$. They alsocharacterized the (1,2)-step competition graphs of tournaments and extendedsome results to the $(i,j)$-step competition graphs of tournaments. In thispaper, the definition of the (1,2)-step competition graph of a digraph isgeneralized to the one of a hypertournament and the $(1,2)$-step competitiongraph of a $k$-hypertournament is characterized. Also, the results are extendedto the $(i,j)$-step competition graph of a $k$-hypertournament.

The (1,2)-step competition graph of a hypertournament