Hypercrosslinked polymers (HCPs) synthesized by copolymerisation of p-dichloroxylene (p-DCX) and 4,4′-bis(chloromethyl)-1,1′-biphenyl (BCMBP) constitute a family of low density porous materials with excellent textural development. Such polymers show microporosity and mesoporosity and exhibit Brunauer–Emmett–Teller (BET) surface areas of up to 1970 m² g⁻¹. The CO₂ adsorption capacity of these polymers was evaluated using a thermogravimetric analyser (atmospheric pressure tests) and a high-pressure magnetic suspension balance (high pressure tests). CO₂ capture capacities were related to the textural properties of the HCPs. The performance of these materials to adsorb CO₂ at atmospheric pressure was characterized by maximum CO₂ uptakes of 1.7 mmol g⁻¹ (7.4 wt%) at 298 K. At higher pressures (30 bar), the polymers show CO₂ uptakes of up to 13.4 mmol g⁻¹ (59 wt%), superior to zeolite-based materials (zeolite 13X, zeolite NaX) and commercial activated carbons (BPL, Norit R). In addition, these polymers showed low isosteric heats of CO₂ adsorption and good selectivity towards CO₂. Hypercrosslinked polymers have potential to be applied as CO₂ adsorbents in pre-combustion capture processes where high CO₂ partial pressures are involved.