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We first derive the recurisions for integer moments of two-typecontinuous-state branching processes in L\'{e}vy random environments. Resultshows that the $n$th moment of the process is a polynomial of the initial valueof the process with at most $n$ degree. Under some natural condition, thecriteria for the existence of $f$-moment of the process are also proved.

Moment properties for two-type continuous-state branching processes in random environments