The present invention provides a thermally curable pressure-sensitive adhesive composition, which, based on the total weight of the composition, comprises the following components: a) 35-99% by weight of a reactive polymethacrylate component having a glass transition temperature Tg of −35° C. to 32° C., and having a reactive functional group which can react with benzoxazine to form an interpenetrating polymer network; and b) 1-65% by weight of a benzoxazine component of the following formula: wherein: X is selected from the group consisting of a covalent bond, C1-C6 alkylene, C3-C10 cycloalkylene group, C═O, S, S═O or O═S═O R1 and R2 are the same or different and independently of each other selected from the group consisting of hydrogen, C1-C6 alkyl, or C5-C14 aryl, and R4 is selected from the group consisting of hydrogen, halogen or C1-C6 alkyl. The present invention also provides an electrically conductive adhesive composition and an adhesive tape comprising the above-described composition, and provides for the use of the composition for preparing membranes used for electronic and electrical products, automobile products and new energy equipment.