Provided are a connector member and a connector that are easy to assemble and capable of adjusting of misalignment or inclination of a fitting axis. In the connector, a first connector member having a first housing is fitted with a second connector member having a second housing and a supporting member that supports the second housing. The first housing is formed with a guide pin, the second housing is formed with a guide-pin guiding part, and the guide-pin guiding part is formed with a guide hole that guides the guide pin. The second housing has a pair of elastic supporting members formed at opposed positions on the supporting member side. When the guide pin is inserted into the guide hole, the guide pin presses the guide hole, the elastic supporting members are elastically deformed, and the second housing is moved, enabling the fitting.