The area of powertrain dynamics has received considerable attention over a number of years. The recent introduction of more stringent emission requirements together with economic pressure has led to a particular focus on increasing powertrain efficiency. This has seen the incorporation of on-board, real-time measurements to predict system behaviour and engine condition. In this domain, accurate models for all powertrain components are important. One strategy to improve accuracy is to evaluate the assumptions made when deriving each model and then to address the simplifications that may introduce large errors. To this end, the aim of the work presented in this dissertation was to investigate the consequences of some of the more common assumptions and simplifications made in low frequency torsional powertrain models, and to propose improved models where appropriate. In particular, the effects of piston-tocylinder friction, crank/gudgeon pin offset, and the torsional behaviour of tyres were studied. Frequency and time domain models were used to investigate system behaviour and model predictions were compared with measurements on a small single cylinder engine. All time domain engine and powertrain models also include a variable inertia function for each reciprocating mechanism. It was found that piston-to-cylinder friction can increase the apparent inertia variation of a single reciprocating engine mechanism. This has implications for the nonlinear behaviour of engines and the drivetrains they are connected to. The effect of crank/gudgeon pin offset also modified the nonlinear behaviour of the mechanism. Though, for typical (small) gudgeon offset values these effects are small. However, for large offset values, achievable practically with crank offset, the modification to the nonlinear behaviour should not be ignored. The low frequency torsional damping properties of a small pneumatic tyre were found to be more accurately represented as hysteretic rather than viscous. Time domain modelling was then used to extend the results to a multi-cylinder engine powertrain and was achieved using the Time Domain Receptance (TDR) method. Various powertrain component TDRs were developed using Laplacians. Powertrain simulations showed that piston-to-cylinder friction can provide additional excitation to the system.