Abstract: The double module of  semi-associative 3-algebras was defined, and the structure of double modules and regular double modules of semi-associative 3-algebras were studied. We prove that for any semi-associative 3-algebra (A,{,,}),  the cycle sum ［,,］_c of the multiplication  {,,} is a 3-Lie multiplication on A, and study  the relation  between derivations of (A,{,,}) and (A,［,,］_c).

Key words: semi-associative 3-algebra, adjoint 3-Lie algebra, double module