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Slip-controlled lock-up clutch systems are very efficient and greatly improve fuel economy. On the other hand, these systems can cause unstable vibrations including those known as “shudder vibrations”. In this study, the authors made a theoretical analysis of these unstable vibrations to clarify the fundamental frictional properties of automatic transmission fluids (ATFs) required for slip-controlled lock-up clutch systems. Based on this analysis, we established lubricant technology having a sufficient anti-shudder property and high torque capacity. Further, we developed a new test apparatus to evaluate the anti-shudder durability for lubricant development.