The paper focuses on the subject of conditional increase of share capital in a joint stock company. Describing the right to take up shares in conditionally increased capital, the author draws attention to the institution of subscription right and presents his conception of subscription right as one of many cases of priority rights in the Polish civil law. Different cases of rights to take up shares granted under the conditional increase of share capital are described in detail. The author also presents arguments for the validity of the view expressed in literature that the right to take up shares in conditionally increased capital puts the rightholder in the position of an offeree to whom the company has previously made an offer to conclude a share subscription agreement.