To provide a new reaction product of a dispersant for crankcases, wherein the above reaction product has a capacity of functioning as an antioxidant while maintaining at least two structural regions, a polar region associating with sludge and a hydrocarbyl region associating with solubility of petroleum by uniting an antioxidant group within the reaction product in order that the dispersant can make sludge floating and act as a chemical substance preventing aggregation of precursors of sludge and soot and that any aggregation of sludge and soot can be easily eliminated from the system by a process like filtering to prevent formation of a harmful substance inside an engine section, and also to provide a new dispersant and a lubrication composition, for example, containing the above dispersant for lubricating an engine.

The reaction product of a dispersant having an antioxidant part is prepared under effective conditions for reacting a hindered phenol-based antioxidant with a reactive dispersant containing a succinic amide-based dispersant or a reactive dispersant containing a Mannich-based dispersant are effectively reacted.