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We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex 𝓧 of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(𝓧') ≅ Hₙ(𝓧)', where Hₙ(𝓧)' is the dual space of the homology group of 𝓧 and Hⁿ(𝓧') is the cohomology group of the dual complex 𝓧'. A Künneth formula for chain complexes of nuclear...