THE CONCEPT OF MAJORITY DOMINATION IN GRAPHS HAS BEEN DEFINED IN AT LEAST TWO DIFFERENT WAYS: AS A FUNCTION AND AS A SET. IN THIS WORK WE EXTEND THE LATTER CONCEPT TO DIGRAPHS, WHILE WE EXTENDED THE FORMER IN ANOTHER PAPER. GIVEN A DIGRAPH D= (V, A), A SET SÍ V IS A MAJORITY OUT-DOMINATING SET (MODS) OF D IF (FORMULA). THE MINIMUM CARDINALITY OF A MAJORITY OUT-DOMINATING SET IN D IS THE SET MAJORITY OUT-DOMINATION NUMBER ¡M+ (D) OF D. IN THIS WORK WE INTRODUCE THESE CONCEPTS AND PROVE SOME RESULTS ABOUT THEM, AMONG WHICH THE CHARACTERIZATION OF MINIMAL MODSS.