In a connector having a wire connection structure of a conductor abutting type, it is an object to decrease the external size of the connector as much as possible without impairing the stability and reliability in a connection between a terminal element and a conductor. A connector (10) is provided with a terminal element (12) including a conductor-connecting section (14) connectable to a conductor (C) of an electric wire (W) and a contact section (16) capable of coming into conductive contact with a corresponding terminal element of a counterpart connector, an electrically insulating body (18) for supporting the terminal element (12) while exposing the conductor-connecting section (14) and the contact section (16), and an abutting member (20) assembled with the body (18) and bringing the wire conductor (C) into abutment with the conductor-connecting section (16) of the terminal element (12) under pressure. The body (18) includes a fitting portion (26) capable of fitting with a counterpart connector while positioning the contact section (16) of the terminal element (12) with respect to the corresponding terminal element. The conductor-connecting section (14) and the contact section (16) of the terminal element (12) are arranged to be aligned with each other in a direction generally orthogonal to a connector fitting direction defined by the fitting portion (26). The connector fitting direction is generally perpendicular to a wire extending direction on the body (18).