The serial harnesses introduced by Hammersley describe the motion of a hypersurface of dimension d embedded in a space of dimension d + 1. The height assigned to each site i of Z(d) is updated by taking a weighted average of the heights of some of the neighbors of i plus a "noise" (a centered random variable). The surface interacts by exclusion with a "wall" located at level zero: the updated heights are not allowed to go below zero. We show that for any distribution of the noise variables and in all dimensions, the surface delocalizes. This phenomenon is related to the so-called "entropic repulsion". For some classes of noise distributions, characterized by their tail, we give explicit bounds on the speed of the repulsion. (C) 2004 Elsevier B.V. All rights reserved.1141175190