Let A and B be operads and let X be an object with an A-algebra and a B-algebra structure. These structures are said to interchange if each operation α:Xn→X of the A-structure is a homomorphism with respect to the B-structure and vice versa. In this case the combined structure is codified by the tensor product A⊗B of the two operads. There is not much known about A⊗B in general, because the analysis of the tensor product requires the solution of a tricky word problem.Intuitively one might expect that the tensor product of an Ek-operad with an El-operad (which encode the multiplicative structures of k-fold, respectively l-fold loop spaces) ought to be an Ek+l-operad. However, there are easy counterexamples to this naive conjecture. In this paper we essentially solve the word problem for the nullary, unary, and binary operations of the tensor product of arbitrary topological operads and show that the tensor product of a cofibrant Ek-operad with a cofibrant El-operad is an Ek+l-operad. It follows that if Ai are Eki operads for i=1,2,…,n, then A1⊗…⊗An is at least an Ek1+…+kn operad, i.e. there is an Ek1+…+kn-operad C and a map of operads C→A1⊗…⊗An.