Let M be a compact hypersurface with boundary ∂M = ∂D1 ∪ ∂D 2 , ∂D 1 ⊂ Π 1 , ∂D 2 ⊂ Π 2 , Π 1 and Π 2 two parallel hyperplanes in R n+1 (n ≥ 2). Suppose that M is contained in the slab determined by these hyperplanes and that the mean curvature H of M depends only on the distance u to Π i , i = 1, 2 and on u. We prove that these hypersurfaces are symmetric to a perpendicular orthogonal to Π i , i = 1, 2, under different conditions imposed on the boundary of hypersurfaces on the parallel planes: (i) when the angle of contact between M and Π i , i = 1, 2 is constant; (ii) when ∂u/∂η is a non-increasing function of the mean curvature of the boundary, ∂η the inward normal; (iii) when ∂u/∂η has a linear dependency on the distance to a fixed point inside the body that hypersurface englobes; (iv) when ∂D i are symmetric to a perpendicular orthogonal to Π i , i = 1, 2.