The torsional vibration phenomenon in the running gear of reciprocating engine systems isusually dealt with by considering a series of constant inertias connected by sections of massless shafting. However in reality, a slider crank mechanism is a vibrating system with varying inertia because the effective inertia of the total oscillating mass of each crank assembly varies twice per revolution of the crankshaft. Large variations in inertia torques can give rise to the phenomenonof secondary resonance in torsional vibration of modern marine diesel engines which can not be explained by conventional theory incorporating only the mean values of the varying inertias. In the past associated secondary resonances and regions of instability tended to be dismissed by most engineers as interesting but of no importance. The situation changed in recent years since there is evidence of the existence of thesecondary resonance effects which could have contributed to a number of otherwise inexplicable crankshaft failures in large slow speed marine engines. The cyclic variation of the polar moment of inertia of the reciprocating parts during each revolution causes a periodic variation of frequency and corres ponding amplitude of vibration of reciprocating engine systems. It also causes an increase in the speed range over which resonance effects are experienced and only a partial explanation of the behaviour of the systems has been worked out. It is impossible to avoid these instabilities by changes in thedesign , unless of course the variations in mass and spring constant can be made zero. In the present paper a critical appraisal of the regions of instability as determined from the equation of motion which takes into account variation of inertia is given. The motion in the form of complex waveforms is studied at different speeds of engine rotation. A comparison of theoretical results with Goldsbrough’s experimental resultsand Gregory’s analysis is included.