The dual mass flywheel especially used in diesel engines has a structurein which the single- mass flywheel is divided into two parts and these twoparts are combined with a curved helical spring. The flywheel is a part thatreduces the speed fluctuations in the crankshaft of the internal combustionengines. In addition to this function, the dual mass flywheel dampens thetorsional vibrations better than the clutch disc springs thanks to the springsystem found in its structure. There are no torsional springs in the disc ofthe clutch system where dual mass flywheel is used. The dual massflywheel is used with a rigid clutch disc without torsion springs. From thispoint of view, it is thought that the clutch dynamics of both systems aredifferent. For this purpose, mathematical models of both systems wereformed. The obtained models were solved after the appropriatetransformations. As a result, it was seen the clutch engagement times arealmost same in both systems. However in the clutch system where the dualmass flywheel is used the clutching process is performed more smoothly.