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This is a rush transcript from "The O'Reilly Factor," January 21, 2008. This copy may not be in its final form and may be updated.

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BILL O'REILLY, HOST: In the "Unresolved Problem" segment tonight: A recent AP poll says 34 percent of Americans do believe in UFOs; 63 percent do not.

But in Stephenville, Texas, 100 miles southwest of Dallas, they do believe. About 40 residents there saw UFOs or say they saw them a few weeks ago. Joining us now from Dallas are two witnesses, Steve Allen and James Hughes.

Mr. Allen, begin with you. Tell us exactly what you saw.

STEVE ALLEN, UFO WITNESS: Yes, sir. Thanks for having us.

Back in January, the 8th, we was at a friend of mine's house and burning some debris and looked off to the east and saw several sets of lights coming towards us. Thought it might have been several aircraft approaching us in some sort of formation. And the lights was more intense and very bright. And they all seemed to be moving at the same speed and altitude and everything, about 3,000 foot above the ground coming at us very fast.

O'REILLY: All right. So you see this thing and, you know, it could be anything. Could be a reflection. Could be anything. But then I understand that you saw military, U.S. military aircraft in proximity to the UFOs?

ALLEN: After it already came by us and did a little flame-job over Stephenville and disappeared, it came back by. And that's when it had the military craft in pursuit, probably four or five seconds behind. But...

O'REILLY: Now you know the military denies that any military aircraft were in the proximity of Stephenville that evening.

ALLEN: Yes, of course.

O'REILLY: Well, you know, it sounds like you might be a conspiratorialist here. Are you positive that U.S. military planes were hovering around or flying around these UFOs?

ALLEN: Yes, absolutely sure. Quite a few people saw the UFO itself, and then many more people saw the jets come past in pursuit. The constable saw it. One of the managers of the airport saw the jets. Quite a people saw that. Several other pilots, also.

O'REILLY: Now Mr. Hughes, you were — you didn't know Mr. Allen, Mr. Hughes, right?

JAMES HUGHES, UFO WITNESS: Correct. I didn't know him at all.

O'REILLY: But you were in the area, too. Mr. Allen was visiting friends. He lives in Glen Rose, I understand. But you're a hometown Stephenville guy.

HUGHES: That's correct.

O'REILLY: What did you see?

HUGHES: Well, you say hometown Stephenville. I was actually two blocks from the center of town, actually, from the courthouse. And I had just walked out of the house, walking a couple of friends to their car, when I looked up. And there was two very large, glowing — I'd call them glowing, burning kind of looking objects, globe-like-looking objects that were just barely moving in the sky and hovering in the sky over my house. And it was pretty startling. It absolutely was.

O'REILLY: Now, when they went away, and then Mr. Allen says they came back, did you see the military aircraft around?

HUGHES: No, I didn't see the military aircraft. And I actually didn't hear any noise at all. These were real low in the sky and very close. And they weren't making any noise at all at that time.

O'REILLY: Were you scared?

HUGHES: I didn't hear any — no, I was actually very curious. I was fascinated, really. I'm used to trying to figure out most things that I see. And when I saw these, and it was something I couldn't explain. And I'm not used to seeing something that I can't explain. So I was fascinated. That's what I was. I was just...

O'REILLY: I believe you guys. I believe you guys saw stuff. I'm not sure about the military. If it's 3,000 feet, sometimes it's hard to identify that, Mr. Allen, you know, what they are.

But I believe you guys saw something. I don't know, obviously, what it is. I can't possibly know that. But do you guys get angry when people go, "Oh, this is a bunch of bologna?" Does that bother you, Mr. Allen?

ALLEN: No, we expected that. And of course, it was up close and personal. The visibility was unlimited and still plenty of sunlight the first time we saw it. So, no, I know what we saw, and lots of other folks saw it.

O'REILLY: All right. Well, we hope that someday it's explained in some context. And gentlemen, we appreciate you coming on and telling everybody what happened down there in Stephenville, Texas. Thanks very much.

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