Abstract: Driving device of a rotating cylinder block (8) of a pump or hydraulic motor whose axis is inclined along an angle that is fixed or that can be adjusted in relation to the axis of rotation XX' of the drive shaft (1) and in which the transmission of the rotation torque from the drive shaft (1) to the cylinder block (8) (pump) and from the cylinder block (8) to the drive shaft (1) (motor) is performed by pistons (5) mounted by connecting ball joints (6) to a pulse plate (4) fixed in rotation with the drive shaft (1). The face (8a) of the cylinder block (8) turned toward the pulse plate (4) carries pairs of diametrically opposed projections (10) located at the entrance of the bores (7) of the cylinder block in which the pistons (5) move, which projections exhibit a concave surface (11) in contact with a surface of the ball joints (6) for connecting the pistons with the pulse plate (4). Applications is to motors and pumps having rotating cylinder blocks.