A process (1, 101, 201) for separating a fibrous target component (21) from textile waste (2, 5) is shown, said textile waste (2, 5) containing the target component (21) and at least one ancillary component (22), whereby the target component (21) consists of water-swellable textile fibers (51) with a density higher than the density of water, the process (1, 101, 201) comprising the steps: a) dispersing the comminuted textile waste (5) in an aqueous solution (7) to obtain a suspension (8) containing the textile waste (5), and b) separating the dispersed textile waste (5) into a high-density target fraction (81) comprising the target component (21), and a low-density residual fraction (82) comprising the at least one ancillary component (22), according to the respective density of said components (21, 22). In order to provide a reliable, fast process for the separation of water-swellable fibers from other textile fibers which are similar in density, it is proposed, that the aqueous solution (7) is an alkaline aqueous solution (7) and the target component fibers (51) are swelled in the alkaline aqueous solution (7) prior to step b), thereby increasing the density and weight of said target component (21) relative to the density and weight of the ancillary component (22).