Grate systems are frequently used today in processes for the thermic treatment of lumpy residues in the first stage of the process. An important partial objective of the thermic treatment is the extensive decomposition of organic substances. Especially with grate systems, numerous influencing possibilities for process control are given. There exists, however, the task, - as with other apparatuses, too -, to optimize the process procedure, correspondingly tuned to the individual properties of the residues. Against this background, the classification of the grate process into these processes is shown, after a short presentation of superior points of view on the thermic treatment processes. Thereafter, model concepts concerning the solid matter conversion in grate systems aw being discussed, whereby first of all theoretical considerations are placed in the forefront. Comprehensive presentations of the experiments will follow in a further report.