The Corex as well as the Finex process today represent an important alternative to the conventional blast furnace route in the field of pig iron production. They are especially characterized by a high flexibility concerning the raw materials they can accept. Compared to the blast furnace process a wide variety of iron ores and coals can be used. The material can be charged directly to the process without pre-treatment, therefore the operation of a coke oven plant can be omitted. Today the Corex process is already commercially applied at five different sites worldwide. There is also one Finex process in operation at large scale. Both processes are relatively new and are constantly subject to further developments and optimization processes. This document deals with the processes occurring in the Corex and Finex melter gasifier, which represents the second unit of the two-stage processes. It is well-known that the movements of the fixed bed play an important role concerning stability and quality of the process. Calculation models and a simulation program have been created in order to allow a rough estimation of the movements of the fixed bed. This diploma thesis gives a detailed description of the established calculation models and of the simulation program.