A compression pendulum mill, for finely grinding mineral materials, of the type comprising: - a cylindrical enclosure provided with a horizontal base (bottom); - a ring-shaped element, concentric with the enclosure and inside the same; - a central rotary shaft; - at least two rollers (18, 19) each rotatably mounted to a pendulum rod (16, 17), a rod (16; 17) and the roller (18; 19) associated therewith forming a pendulum; - pivot connection means (14, 15) between the pendulums and the shaft, for rotating the rollers (18, 19) about the shaft on the one hand and around themselves on the other hand, so as to enable crushing of the materials located between the rollers (18, 19) and the internal wall of the ring; - means for supporting and holding the shaft; - means for rotatably driving the shaft, the means for supporting and holding the shaft being external to the enclosure, characterised in that the means for supporting and holding the central shaft are, on the one hand, independent of the enclosure and, on the other hand, include means for driving the central shaft, in the form of a rotary hearth associated with a speed reducer assembly, itself associated with the means for driving the central shaft, said hearth both ensuring transmission of rotation of the motor, and support and guidance of the central shaft, said hearth being rotatably mounted in a fixed pivot disposed in the reducer which itself is fastened to a rigid external support provided therefor. - a cylindrical enclosure provided with a horizontal base (bottom); - a ring-shaped element, concentric with the enclosure and inside the same; - a central rotary shaft; - at least two rollers (18, 19) each rotatably mounted to a pendulum rod (16, 17), a rod (16; 17) and the roller (18; 19) associated therewith forming a pendulum; - pivot connection means (14, 15) between the pendulums and the shaft, for rotating the rollers (18, 19) about the shaft on the one hand and around themselves on the other hand, so as to enable crushing of the materials located between the rollers (18, 19) and the internal wall of the ring; - means for supporting and holding the shaft; - means for rotatably driving the shaft, the means for supporting and holding the shaft being external to the enclosure, characterised in that the means for supporting and holding the central shaft are, on the one hand, independent of the enclosure and, on the other hand, include means for driving the central shaft, in the form of a rotary hearth associated with a speed reducer assembly, itself associated with the means for driving the central shaft, said hearth both ensuring transmission of rotation of the motor, and support and guidance of the central shaft, said hearth being rotatably mounted in a fixed pivot disposed in the reducer which itself is fastened to a rigid external support provided therefor. the means for supporting and holding the shaft being external to the enclosure, characterised in that the means for supporting and holding the central shaft are, on the one hand, independent of the enclosure and, on the other hand, include means for driving the central shaft, in the form of a rotary hearth associated with a speed reducer assembly, itself associated with the means for driving the central shaft, said hearth both ensuring transmission of rotation of the motor, and support and guidance of the central shaft, said hearth being rotatably mounted in a fixed pivot disposed in the reducer which itself is fastened to a rigid external support provided therefor.