•Strongly Ruelle–Takens chaos, strongly Auslander–Yorke chaos and Poincare chaos are studied on the product of semiflows.•It is proved that if the finite or the countably infinite product of semiflows is strongly Ruelle–Takens chaotic (resp., strongly Auslander–Yorke chaotic and Poincare chaotic) then at least one of the factors is so.•Examples/counterexamples are also provided related to our results. In this paper, we study strongly Ruelle–Takens chaos, strongly Auslander–Yorke chaos and Poincaré chaos on the product of semiflows. It is proved that if the finite product or the countably infinite product of semiflows is chaotic then at least one of the factors is chaotic. We also provide necessary examples/counterexamples, wherever possible, related to our results.