A cable connecting apparatus comprising; a plug type connector having a connectively engaging portion on which a plurality of plug contacts (15,16) are arranged to be connected with a plurality of cables, and a receptacle type connector having a housing on which an opening through which the connectively engaging portion of the plug type connector is inserted in the housing is provided to be formed at an end portion of the housing and a plurality of receptacle contacts (34,35) arranged in the housing for coming into press-contact with the plug contacts (15,16) arranged on the connectively engaging portion of the plug type connector inserted in the housing through the opening provided thereon, characterized in that said receptacle contacts (34, 35) include a plurality of first contacts, each of which has first and second contacting portions (41,42) operative to be opposite to each other with the connectively engaging portion of the plug type connector inserted in the housing through the opening provided thereon between, said first and second contacting portions (41,42) having respectively first and second contacting points (43, 44), a distance from the end portion of the housing at which the opening is formed to said first contacting point being shorter than a distance from the end portion of the housing at which the opening is formed to said second contacting point, said first contacting point being operative to come into press-contact with the plug contact on the side of a first surface of the connectively engaging portion of the plug type connector and said second contacting point being operative to come into press-contact with the plug contact on the side of a second surface opposite to the first surface of the connectively engaging portion of the plug type connector, and a plurality of second contacts, each of which has third and fourth contacting portions (47,48) operative to be opposite to each other with the connectively engaging portion of the plug type connector inserted in the housing through the opening provided thereon between, said third and fourth contacting portions (47,48) having respectively third and fourth contacting points (49,50), a distance from the end portion of the housing at which the opening is formed to said third contacting point is longer than a distance from the end portion of the housing at which the opening is formed to said fourth contacting point, said third contacting point being operative to come into press-contact with the plug contact on the side of the first surface of the connectively engaging portion of the plug type connector and said fourth contacting point being operative to come into press-contact with the plug contact on the side of the second surface opposite to the first surface of the connectively engaging portion of the plug type connector, and in that the plug contacts include a plurality of third contacts and a plurality of fourth contacts, which are arranged one after the other in a direction along which the plug contacts (15,16) are arranged, each of said third contacts having a cable connecting portion with which the cable is connected, a first contact-receiving portion with which one of the first and second contacting points (43,44) of the first contact comes into press-contact and a second contact-receiving portion folded back from the first contact-receiving portion to stick to the first contact-receiving portion, with which the other of the first and second contacting points (43,44) of the first contact comes into press-contact, each of said fourth contacts having a cable connecting portion with which the cable is connected, a third contact-receiving portion with which one of the third and fourth contacting points (49,50) of the second contact comes into press-contact and a fourth contact-receiving portion folded back from the third contact-receiving portion to stick to the third contact-receiving portion, with which the other of the third and fourth contacting points (49,50) of the second contact comes into press-contact, and a top end portion of the second contact-receiving portion of each of said third contacts and a top end portion of the fourth contact-receiving portion of each of said fourth contacts being provided to be partially surrounded by insulating material forming the connectively engaging portion of the plug type connector, and in that the second contact-receiving portion folded back from the first contact-receiving portion of the third contact and the fourth contact-receiving portion folded back from the third contact-receiving portion of the fourth contact are provided respectively on the first and second surfaces opposite to each other of the connectively engaging portion of the plug type connector.