The internal kink mode is commonly present in tokamak plasmas and is often responsible for sawtooth instabilities. The presence of fast ions in the plasma, such as those generated by auxiliary heating, may not only affect sawtooth behaviour but also cause the appearance of fishbone oscillations which are caused by different branches of the internal kink dispersion relation. There are principally two different methods that are used to analyse the internal kink mode stability in the presence of fast ions. The first is based on a perturbative approach and in this case, the fast ions' energy functional is taken as a perturbation of the ideal MHD functional. The use of numerical codes like the new version of the CASTOR-K code then allows an accurate calculation of the perturbation on the mode growth rate. The second method is based on a variational formulation where the full dispersion equation including diamagnetic effects is solved using simplified expressions for the fast ions' energy functional and the fast ions' distribution function. The marginal stability equation allows then the determination of the regions of stability for each of the solutions in the space of parameters. In this paper both methods are described and applied to analyse JET experiments were both sawteeth and fishbone stability changed during the discharge.