A hybrid drill bit includes both fixed cutting elements and rotational cutting elements thereon. The fixed cutting elements are affixed to a bit body and define a peripherally-located fixed cutting structure disposed radially outward of the rotational cutting elements. The rotational cutting elements define a centrally-located counter-rotational cutting structure including two hemispherical counter-rotational cutting members mounted for counter-rotation with respect to one another on an axis generally perpendicular to a bit body rotational axis.