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Abstract Let ( A 0 , A 1 ) $(A_{0}, A_{1})$ be a compatible couple of normed spaces. We study the interrelation of the general K-interpolation spaces of the couple ( A 0 + A 1 , A 0 ∩ A 1 ) $(A_{0}+A_{1}, A_{0} \cap A_{1})$ with those of the couples ( A 0 , A 1 ) $(A_{0}, A_{1} )$ , ( A 0 + A 1 , A 0 ) $(A_{0}+A_{1}, A_{0} )$ , ( A 0 + A 1 , A 1 ) $(A_{0}+A_{1}, A_{1} )$ , ( A 0 , A 0 ∩ A 1 ) $(A_{0}, A_{0} \cap A_{1})$ , and ( A 1 , A 0 ∩ A 1 ) $(A_{1}, A_{0} \cap A_{1})$ .