Twin-wire presses are disclosed for dewatering fiber suspensions comprising endless upper and lower wires defining a dewatering space, upper and lower wire guides for guiding the wires obliquely towards the inlet end of the dewatering space, and upper and lower wedge-shaped seals extending from an inlet box towards the dewatering space inlet to create a seal in the tapering space between the wires and the fiber suspension entering the dewatering space. The inner surfaces of the wedge-shaped seals define a passage for the fiber suspension and the outer surfaces extend at an acute angle towards the inner surfaces so that at least part of the seals are sealed against the wires and the distance between the inner surfaces of the seals is substantially equal to the distance between the wires at the dewatering space inlet.