Methods are provided for removing CO2 and/or H2S from a gas phase stream, such as a refinery flue gas stream, a coal-fired or petroleum-burning power plant, or a natural gas stream. A gas phase stream containing CO2 and/or H2S can be contacted under effective conditions with an aqueous slurry of supported amine particles. The CO2 and/or H2S can react with the supported amines to form bicarbonates, carbonates, carbamates, sulfide salts, or other species. Because the amine is part of, bonded to, or otherwise supported on a particulate substrate, the reaction product from the amine reaction can also remain bound to the particle. After reacting supported amines with CO2 and/or H2S captured from a gas stream, the supported amines particles can be separated from the aqueous slurry environment for regeneration of the supported amine and release of the CO2 and/or H2S.