A first connector housing (1) accommodates substrates (3), and pressing portions (7) extend on opposite sides of the substrates (3). Terminal fittings (5) are accommodated in the second housing (2) and are provided with contact pieces (9) for contacting foil-shaped terminals (4) on outer surfaces of the substrates (3). A contact portion (21) of each elastic contact piece (9) normally is retracted and not in contact with the corresponding terminal (4). When the housings (1, 2) are fitted to each other, the pressing portions (7) press the contact pieces (9) toward the substrates (3), thereby elastically deforming them toward the substrates (3), whereby the contact portions (21) are brought into contact with the terminals (4).