A clamp assembly, for a laying tower for laying continuous, elongated members in a body of water, has a supporting frame; and three clamping units arranged in series to simultaneously clamp and release a continuous, elongated member extending along a given axis, and each having at least two opposite jaws, and self-adjusting mechanisms, each of which is interposed between a respective jaw and the supporting frame, has a spring, and allows an adjustment movement of the respective jaw with respect to the supporting frame in a direction parallel to the axis, under the weight of the continuous, elongated member, and in opposition to the spring, when the continuous, elongated member is gripped simultaneously by the clamping units.