  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.
