Like Benefiel, both Jordan and Cox said the Bible includes references to exorcism, and skeptics must take up the issue with that holy text since it is what their respective organizations are founded upon.
"People who don't want to believe in (demonic) possession need to talk to Christ," Jordan said.
"It's actually normal Christianity. All churches should be doing this, but they skip around it. Jesus told us to do it, and we have this power from Jesus Christ and the cross," he said.
Meanwhile, Jordan said he considers himself Southern Baptist although he doesn't have a church home. He said he has been ordained through two ministerial associations: Victory New Testament Fellowship in Mesquite, Texas, and St. Luke's Christian Ministerial Association in Georgia. He said he attended two different theological seminaries and was never taught anything about fighting evil forces such as demons.
He said he conducted research on his own and deduced that there were several ways people open themselves to demonic possession.
One way is dabbling in the occult, which could be anything from Ouija boards to participating in fantasy role-playing games, Jordan said. He said this also could include movies and books such as "Harry Potter," which feature the occult prominently or glorify evil and violence in some way. Other ways include sexual immorality and illicit drugs, Jordan said.
Jordan said out of more than 1,000 e-mails about possible demonic possession, he determined that only one seemed to be a clear-cut case of possession.
He said many people mistake severe depression and its symptoms for demonic possession. But he said he tells people to look for several signs of demonic possession or demonic presence including supernatural or paranormal happenings such as levitation. Jordan said another sign of possession is some action that is impossible according to the laws of the universe, a la the spinning head of the young girl character in "The Exorcist" movie.
By contrast, Cox said he's seen nothing that compares to the scenes in "The Exorcist" during his deliverance sessions. He said there is an occasional outburst from someone his prayer leaders are praying for, but "we haven't seen a person's head rotate 360 degrees."
Cox said his ministry teaches that signs of a person under the influence of an unclean spirit could be things such as rage, self-hate, hate, pornography/sexual addiction, hoarding and other things he has placed on a "problem list."
"The root of some of these problems is spiritual," he said.
Movies: Help or hindrance?
Jordan said he is aware of the public's curiosity about exorcism.
The movie "The Exorcist" with then-child actor Linda Blair was followed by other similar films, and Hollywood's propensity for stories about exorcism continues today. In recent years, exorcism has been the subject of such films as 2005's "The Exorcism of Emily Rose" and a movie that premiered this past August called "The Last Exorcism."
Jordan said the movies appear to draw audiences because of the mystery that surrounds exorcism.
He said the movies hinder his ministry and Christianity when they show the devil having more power than God.
"They portray Christ as inferior to Satan, and I don't like that," Jordan said.
Finding middle of two extremes
The Rev. Bobby Kelly, the Ruth Dickenson Professor of Bible at Oklahoma Baptist University, said he thinks there is a tendency for people to go to one of two extremes when it comes to the subject of exorcism.
One extreme is the denial of demonic activity, and the other is "finding demons everywhere," Kelly said.
Kelly, a Southern Baptist, said what people want to believe is up to them, but the Bible does reference exorcism. He said one example can be found in Mark 5:1-19, which describes Jesus casting "legion" or numerous unclean spirits out of a man into a herd of swine. In another instance, Mark 1:23-27, Jesus rebukes an unclean spirit in the synagogue and casts it out of a man.
"If Jesus did anything in His day-to-day ministry, He cast out demons and unclean spirits," Kelly said.
Kelly said Western culture does not easily recognize demonic activity because people want evidence of it.
Kelly said he does not reject the idea of demonic activity because of the biblical references, but he said he would caution anyone from the tendency to find "a demon under every rock."
Denying that it exists also could be problematic.
"On the other hand, there are forces in the world that are set against what is good. To deny the existence of those forces is to allow them to gain the upper hand."
Kelly said he can appreciate Jordan, whom he has never met, for attempting to open up a discussion about "something that is clearly a danger (evil) in our world today."