The invention relates to a method of making an absorbent article, in which a composite elastic member (1) is attached to a topsheet, backsheet, core or any combination thereof. The composite elastic member (1) comprises a first, relatively unextensible layer (7, 15) and a second, elastically extensible layer (11). The elastically extensible layer (11) is attached to the unextensible layer (7, 15) in its relaxed state. The composite elastic member (1) is supplied from a supply station while in its relatively unelongatable state and is activated by stretching or 'ring rolling' just prior to, or shortly after attaching the composite elastic member (1) to the topsheet, backsheet, core or any combination thereof. Alternatively, the method according to the invention comprises imparting extensibility to the composite elastic member (1) in a manner such that the composite elastic member (1) remains unelongatable in its longitudinal direction, followed by applying the composite elastic member (1) to the topsheet, backsheet core or any combination thereof. The method according to the invention allows supply of an elastic member (1) without need for tension control means and allows controlled design of the elastic properties of an absorbent article.
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