The synthesis of polyHIPEs with bimodal pore-size distribution and very high specific surface areas up to 1210 m² g^-1 is reported. Monolithic polyHIPE precursors were swollen, and subsequently the polymeric network was crosslinked in the expanded state by internal and external electrophiles under catalysis of a Lewis acid leading to hypercrosslinked polymers of the Davankov type. The materials have a high n-butane uptake (34 wt% at 298 K) and moderate hydrogen storage capacity (2.02 wt% at 19.5 bar and 77.4 K). According to water adsorption isotherms, the inner surface area of the systems is highly hydrophobic shifting the adsorption branch to relative humidities of 0.8. The hierarchical organization of the system with transport macropores and highly microporous walls leads to an enhanced n-butane adsorption.