Let G be a finite group and (K, O, k) be a p-modular system "large enough". Let R = O or k. There is a bijection between the blocks of the group algebra RG and the central primitive idempotents (the blocks) of the so-called cohomological Mackey algebra coµ R (G). Here, we prove that a so-called permeable derived equivalence between two blocks of group algebras implies the existence of a derived equivalence between the corresponding blocks of cohomological Mackey algebras. In particular, in the context of Broué's abelian defect group conjecture, if two blocks are splendidly derived equivalent, then the corresponding blocks of cohomological Mackey algebras are derived equivalent.The main result of this paper is the following theorem which settles the question for the cohomological Mackey algebra in the case of a splendid equivalence (see [14]): Theorem 1.2. Let G and H be two finite groups, let b be a block of RG and c be a block of RH. If RGb and RHc are splendidly derived equivalent, then D b (coµ R (G)ι(b)) ∼ = D b (coµ R (H)ι(c)).