Abstract: A connector unit of the multiple-connection, rapid-engagement type includes a first connector part and a second connector part which can be coupled face to face as a result of a relative movement along a general axis of the first connector part. The second connector part is carried by a movable body adapted to stop close to the first connector part so that these face each other. The connector parts include mutual centring means. One of these two connector parts is movable transverse the direction of coupling to compensate for any transverse misalignment relative to this direction. The movable connector part is carried by an auxiliary support structure with the interposition of resiliently yielding members so as to be swingable relative to the support structure. These resilient members are preloaded so as, in their undeformed condition, to define a rest position corresponding to the aligned condition of the two connector parts.