A double-acting hydraulic pressure intensifier includes a supply connection, a return connection, a high-pressure connection. An intensifier piston assembly includes a low-pressure piston arranged in a low-pressure cylinder and two high-pressure pistons connected to the low-pressure piston each arranged in a high-pressure cylinder. A switching valve assembly includes a displace able, hydraulically controlled valve element which on its two opposite sides in the direction of displacement has control pressure chambers with pressure application areas of different sizes, namely, a first control pressure chamber with a smaller pressure application area and a second control pressure chamber with a larger pressure application area. A stop plug is arranged between the second control pressure chamber and the supply connection.