Combustion of woody biomass in a fixed-bed configuration could play an important role in the development of small-scale combined-heat-and-power solutions, such as externally-fired micro-gas turbines. However, many challenges still remain with regard to the complexity of maintaining high availability with an acceptable fuel flexibility, as ash transformations in the fuel bed can cause serious problems for the robustness of the process as well as for downstream components. In this work, fixed-bed combustion of two woody biomasses of different ash contents is studied experimentally and numerically in an attempt to advance the understanding of ash-related disturbances. A mathematical model for fixed-bed conversion of biomass is extended to account for ash transformations on both the single-pellet level and the bed level, and the predictions from this model are assessed against the experimental results. The agreement between simulations and experiments is good for low air-flow rates, whereas additional considerations are needed for air-flow rates closer to the stoichiometric limit. Although there was no catastrophic slagging observed in the experiments, the capabilities of the model to describe effects of such slagging, down to only slightly reduced combustion rates due to milder ash transformations, are confirmed by the simulations.