At length [Sauron] resolved that no others would serve him in this case but his mightiest servants, the Ringwraiths, who had no will but his own, being each utterly subservient to the ring that had enslaved him, which Sauron held. ("The Hunt for the Ring", Unfinished Tales)

[Had Frodo claimed the Ring in Mount Doom without interference by Gollum, the Nazgul would have been dispatched to stall him until Sauron himself could come.] I do not think they could have attacked him with violence, nor laid hold upon him or taken him captive; they would have obeyed or feigned to obey any minor commands of his that did not interfere with their errand–laid upon them by Sauron, who still through their nine rings (which he held) had primary control of their wills. (Letter 246, September 1963)