The present invention provides a connector which can take an EMI measure for the first and second housings and can move the second housing with respect to the first housing. The connector comprises a plug which is provided so as to be movable with respect to the socket; a plurality of socket terminals which are resiliently deformed with a movement of the plug; a first socket side shield member which covers an outer circumference surface in the width direction of the socket; a plurality of plug terminals which are in contact with each of the socket terminals when the plug is mated with the socket; a plug side shield member which covers an outer circumference surface in the width direction of the plug; and first and second shield conductive portions which are in contact with each of the shield members and are resiliently deformed as the plug is moved.