A process for the production of synthetically produced methane (57)/gaseous and/or liquid hydrocarbons (114, 115, 116, 117). For this purpose, hydrogen (44, 84, 150) from an electrolytic arrangement (41, 81, 151, 159) which is operated by means of regeneratively generated electric energy and carbon dioxide (19, 46, 86) are synthesized in a methane synthesis (FIGS. 2-48) or Fischer-Tropsch synthesis (FIGS. 3-96) or other suitable hydrocarbon synthesis, the carbon dioxide (19, 46, 86) being produced from an air/gas flow (3, 134) by means of a carbon dioxide recovery system (FIG. 1). The carbon dioxide (19, 46, 86) is obtained from the air/gas flow (3, 134) in the carbon dioxide recovery system (FIG. 1) by way of a reversible adsorption process. Also a production system (57) for the production of synthetically produced methane/gaseous and/or liquid hydrocarbons (114, 115, 116, 117), in particular for carrying out the production process according to the invention, comprising an electrolytic arrangement (41, 81, 151, 159) which is operated by means of regeneratively generated electric energy (42, 82, 153) for producing hydrogen (44, 84, 150), a carbon dioxide recovery system (FIG. 1) for producing carbon dioxide (19, 46, 86) from an air/gas flow (3, 134) and a methane (FIG. 2) or Fischer-Tropsch synthesis (FIG. 3) or any other suitable hydrocarbon synthesis for synthesizing hydrogen (44, 84, 150) and carbon dioxide (19, 45, 86) to methane (57)/gaseous and/or liquid hydrocarbons (114, 115, 116, 117).