A self-propelled bagging machine for storing grain in a sleeve (unfolding plastic film pipe or silo bag) made up of an upper receiving hopper which outlet leads to a grain discharge tunnel over which such folded sleeve fits, all of this mounted on a chassis equipped with running gear and dragging pole, where such hopper outlet comprises a wall that is transversally connected to the hopper according to a downward slant plane leading to the discharge tunnel arranged under the vertical projection of the mouth of said hopper, and where such running gear comprises a back single-shaft running gear that is connected to the wheels, and a smaller front steering running gear; such grain bagging machine further includes: a dual compensated braking device made up of an adjustable primary hydraulic braking mechanism and an adjustable secondary hydraulic braking mechanism which act simultaneously on the back shaft of the bagging machine, and where a mechanic articulation mounted on the chassis in such a way that it is sensitive to pulling variations during the machine operation activates an inverted operation hydraulic pump for reception/release of braking fluid from/to the secondary braking mechanism circuit for braking compensation. Dual compensated braking device to be applied to the self-propelled grain bagging machine described above.