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Under natural conditions, we proved the exponential ergodicity in Wassersteindistance of two-type continuous-state branching processes in L\'evy randomenvironments with immigration. Furthermore, we expressed accurately theparameters of the exponent. The coupling method and the conditioned branchingproperty play an important role in the approach. Using the tool ofsuperprocesses, the ergodicity in total variance distance is also proved.

Wasserstein-type distances of two-type continuous-state branching processes in L\'{e}vy random environments