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We introduce a new class of operators “ DP u( E ,  Y )” which lives between the class of Dunford-Pettis, the class of AM-compact operators and that of order weakly compact “ L owc( E ,  Y )”, more precisely we have “ DP  ( E ,  Y ) ⊂  DP u( E ,  Y ) ⊂  L owc( E ,  Y )” and “ AM cp( E ,  Y ) ⊂  DP u( E ,  Y ) ⊂  L owc( E ,  Y )”, where  DP  ( E ,  Y ),  AM cp( E ,  Y ) denote the class of Dunford-Pettis operators, AM-compact operators, respectively. And we study some of its properties, like the domination problem and the relations between other classes of operators.

On the class of U-Dunford-Pettis operators