This article illustrates the appearance and electrohydrodynamic consequences of concentration polarization (CP) in hierarchically structured monolithic fixed beds used as stationary phases in CEC and related electrical-field-assisted separation techniques. Subject of the investigation are silica-based monoliths in capillary format with a bimodal pore size distribution. Ion-permselectivity in the intraskeleton pore space together with diffusive and electrokinetic transport induces depleted and enriched CP zones at the anodic and cathodic interfaces, respectively, of the cation-selective mesoporous skeleton. The extent of electrical-field-induced CP is shown to be governed by the fluid phase ionic strength, which tunes the ion-permselectivity of the mesoporous monolith skeleton via local electrical double layer overlap, and by the applied electrical field strength, which determines local transport. The analysis of quantitative confocal laser scanning microscopy data, resolving CP on the local skeleton scale, indicates that at sufficiently high field strength a transition from intraskeleton to interskeleton boundary-layer-dominated transport of charged species occurs. This transition is correlated to the onset of macroscopically measured, nonlinear EOF velocities, whose occurrence is explained in the framework of a nonequilibrium electroosmotic slip. it is shown that the onset of nonlinear electrokinetics in the system can be tuned by properties of the BGE, particularly buffer pH, which modulates the pH-dependent surface charge density and consequently the ion-permselective skeleton's charge selectivity. Finally, the CP dynamics of monolithic and particulate fixed beds are compared, and the observed differences are related to the specific morphologies of the two hierarchical fixed bed structures.