The use of GaAs high electron mobility transistors (HEMTs) in monolithic microwave integrated circuits (MMICs) presents significant challenges to modelling intermodulation distortion performance. It is important that the distortion can be accurately simulated, to avoid the cost of prototyping MMICs and to meet the increasingly stringent low distortion requirements of modern communication system standards. This necessitates the careful consideration of the method used to characterise and extract models from HEMTs. The challenge is to provide a high-order nonlinear model that is accurate over a full spectrum of frequencies. This paper presents measurements of the complicated behavior of HEMT devices. Third-order distortion is seen to sometimes depend on higher-order nonlinearity. In addition, the HEMTs exhibit dispersion in their drain current characteristics up to GHz frequencies due to anomalous effects such as semiconductor charge trapping. Methods to characterise HEMTs are discussed and their applicability is pointed out. In particular, a characterisation method for HEMTs should be able to extract nonlinearities up to a sufficiently high order for the required application, and thus should have high dynamic range. In addition to magnitude, it should be able to measure phase information. It is important that the measurements can be performed at frequencies higher than those affected by dispersion, and high enough that device reactive nonlinearities can be measured. The HEMTs are characterised using a number of methods to show the importance of these considerations.