Abstract: Methods and apparatus for rotating a stripper assembly in use with a rotating drilling head. A drive system is disposed external to the rotating drilling head and generates rotational motion to match the rotation of a drillstring running through the rotating drilling head. A connection transfers rotational motion from the drive system to the stripper assembly. In one embodiment, the drive system comprises a housing disposed about the drillstring and a one or more contact members connected to said housing and operable to contact the drillstring. One or more biasing members urge the contact members into contact with the drillstring so as to transfer rotational motion from the drillstring to the housing.