Process for producing methane or methanol, said process comprising the steps of: i) conducting a solid renewable feedstock to a thermal decomposition step, this being a pyrolysis step or a hydrothermal liquefaction step, for producing: a first off-gas stream comprising hydrocarbons, a solid carbon stream, and optionally a first liquid oil stream; upgrading the first off-gas stream by conducting it to a hydro/deoxygenation (HDO/DO) step i.e. hydrodeoxygenation or deoxygenation step in which said HDO/DO step is conducted in the absence of steam, and a subsequent separation step, for generating water, a second liquid oil stream and an upgraded first off-gas stream; ii) conducting the first off-gas stream or the upgraded first off-gas stream to an olefin removal step, for generating a further upgraded first off-gas stream which is free of olefins; iii-1) conducting the first off-gas stream, or the upgraded first off-gas stream, or the further upgraded first off-gas stream, to a methanation step under the generation of steam for producing said methane; or iii-2) conducting the first off-gas stream, or the upgraded first off-gas stream, or the further upgraded first off-gas stream, to a steam reforming step for producing a methanol synthesis gas and subsequently conducting the methanol synthesis gas to a methanol synthesis step under the generation of steam for producing said methanol; iv) conducting steam, such as at least a portion of the steam generated in step iii-1) or iii-2), to an electrolysis step for producing an oxygen stream and a hydrogen stream; v) conducting at least a portion of the hydrogen stream from the electrolysis step to any of the: thermal decomposition step including HDO-step, olefin hydrogenation step, methanation step, methanol synthesis step, or combinations thereof.