Since only little is known in the field of Solid Oxide Fuel Cell (SOFC) operation about internal reforming of methane at present, the aim of this thesis study is to conduct a detailed investigation delivering the basis for further experimental and theoretical work. Also information is required if the concept of internal reforming has technical development potential. The thesis is arranged into two major parts being a thermodynamic investigation and an application of a suitable kinetic model. Pure methane tends to decompose at the high operation temperatures of the SOFC (about 950°C) thus forming solid carbon. Therefore it is necessary to include a fuel preparation process delivering H2 and CO that can be utilized by the SOFC. The fuel processing can either be carried out by steam reforming or partial oxidation. It is shown by a thermodynamic investigation that fuel processing by partial oxidation yields a fuel gas of inferior quality than fuel processing by steam reforming. The kinetic part contains the application of a model describing the chemical and electrochemical conversion occuring in the SOFC as detailed as possible at present. This model is used to investigate the thermal behaviour of an SOFC process referring to technical operation parameters. It is shown that internal reforming has technical development potential although a lot of care must be paid to the heat management. Particular operation conditions might exist where the highly endothermic steam reforming process could cause a breakdown of the complete fuel cell process due to its enormous local cooling effect.