A fundamental analysis of single-component and binary CO2 and H2O adsorption of amine-functionalized nanofibrillated cellulose is carried out in the temperature range of 283-353 K and at CO2 partial pressures in the range of 0.02-105 kPa, where the ultralow partial pressure range is relevant for the direct capture of CO2 from atmospheric air. Single-component CO2 and H2O adsorption experimental data are fitted to the Toth and Guggenheim-Anderson-de Boer models, respectively. Corresponding heats of adsorption, derived from explicit solutions of the van't Hoff equation, are -50 kJ/mol CO2 and -48.8 kJ/mol H2O. Binary CO2/H2O adsorption measurements for humid air reveal that the presence of H2O at 2.55 kPa enhances CO2 adsorption, while the presence of CO2 at 0.045 kPa does not influence H2O adsorption. The energy demand of the temperature-vacuum-swing adsorption/desorption cycle for delivering pure CO2 from air increases significantly with H2O adsorption and indicates the need to reduce the hygroscopicity of the adsorbent.