Most tissues in multicellular organisms are maintained by continuous cell renewal processes. However, high turnover of many cells implies a large number of error-prone cell divisions. Hierarchical organized tissue structures with stem cell driven cell differentiation provide one way to prevent the accumulation of mutations, because only few stem cells are long lived. We investigate the deterministic dynamics of cells in such a hierarchical multi compartment model, where each compartment represents a certain stage of cell differentiation. The dynamics of the interacting system is described by ordinary differential equations coupled across compartments. We present analytical solutions for these equations, calculate the corresponding extinction times and compare our results to individual based stochastic simulations. Our general compartment structure can be applied to different tissues, as for example hematopoiesis, the epidermis, or colonic crypts. The solutions provide a description of the average time development of stem cell and non stem cell driven mutants and can be used to illustrate general and specific features of the dynamics of mutant cells in such hierarchically structured populations. We illustrate one possible application of this approach by discussing the origin and dynamics of PIG-A mutant clones that are found in the bloodstream of virtually every healthy adult human. From this it is apparent, that not only the occurrence of a mutant but also the compartment of origin is of importance.