Hydraulic shock-absorber comprising an outer cylindrical tube extending along a longitudinal axis (z), an inner cylindrical tube coaxial with the outer cylindrical tube and defining therewith an annular chamber which is filled in a top portion thereof with a compressible fluid, a rod arranged coaxially with said outer and inner cylindrical tubes (12, 14) and partially protruding from the top end of these latter, a main piston that is slidably mounted in the inner cylindrical tube along said longitudinal axis (z) and is fixed to the rod, the main piston dividing an inner volume of the inner cylindrical tube into an extension chamber and a compression chamber, both containing an incompressible damping fluid, a valve assembly (28a, 28b) mounted on a bottom wall of the inner cylindrical tube and comprising a first compression valve configured as a non-return valve allowing the flow of the damping fluid only in the direction from the compression chamber to the annular chamber during the compression phase of the shock-absorber and a first intake valve configured as a non-return valve allowing the flow of the damping fluid only in the direction from the annular chamber to the compression chamber during the extension phase of the shock-absorber, wherein said first compression valve comprises at least one first closure element, which is configured to keep at least one first through hole provided in the bottom wall of the inner cylindrical tube normally closed and to deform or displace elastically, from a given pressure value in the compression chamber, to allow the flow of the damping fluid through said at least one first through hole from the compression chamber to the annular chamber, a cup-shaped body mounted in the inner cylindrical tube, coaxially therewith, inside the compression chamber, and an auxiliary piston that is rigidly connected to the main piston and is configured to slide in the cup-shaped body at least during a final section of the compression phase of the shock-absorber, and wherein the cup-shaped body comprises a lateral wall, separate from the inner cylindrical tube, and a bottom wall, said lateral wall and said bottom wall defining, together with the auxiliary piston, a working chamber wherein the damping fluid is compressed by the auxiliary piston when the latter slides in the cup-shaped body towards the bottom wall thereof, characterized in that it further comprises a second compression valve configured as a non-return valve allowing the flow of the damping fluid only in the direction from the working chamber of the cup-shaped body towards a lower portion of the compression chamber comprised between the bottom wall of the cup-shaped body and the bottom wall of the inner cylindrical tube, wherein said second compression valve comprises at least one second closure element configured to keep at least one second through hole provided in the bottom wall of the cup-shaped body normally closed and to deform or displace elastically, from a given pressure value in the working chamber of the cup-shaped body, to allow the flow of the damping fluid through said at least one second through hole from the working chamber to said lower portion of the compression chamber, and wherein said at least one second closure element is arranged outside the cup-shaped body, namely underneath the bottom wall of the cup-shaped body. an outer cylindrical tube extending along a longitudinal axis (z), an inner cylindrical tube coaxial with the outer cylindrical tube and defining therewith an annular chamber which is filled in a top portion thereof with a compressible fluid, a rod arranged coaxially with said outer and inner cylindrical tubes (12, 14) and partially protruding from the top end of these latter, a main piston that is slidably mounted in the inner cylindrical tube along said longitudinal axis (z) and is fixed to the rod, the main piston dividing an inner volume of the inner cylindrical tube into an extension chamber and a compression chamber, both containing an incompressible damping fluid, a valve assembly (28a, 28b) mounted on a bottom wall of the inner cylindrical tube and comprising a first compression valve configured as a non-return valve allowing the flow of the damping fluid only in the direction from the compression chamber to the annular chamber during the compression phase of the shock-absorber and a first intake valve configured as a non-return valve allowing the flow of the damping fluid only in the direction from the annular chamber to the compression chamber during the extension phase of the shock-absorber, wherein said first compression valve comprises at least one first closure element, which is configured to keep at least one first through hole provided in the bottom wall of the inner cylindrical tube normally closed and to deform or displace elastically, from a given pressure value in the compression chamber, to allow the flow of the damping fluid through said at least one first through hole from the compression chamber to the annular chamber, a cup-shaped body mounted in the inner cylindrical tube, coaxially therewith, inside the compression chamber, and an auxiliary piston that is rigidly connected to the main piston and is configured to slide in the cup-shaped body at least during a final section of the compression phase of the shock-absorber, and