DHAHRAN, Saudi Arabia, Jan. 20— Many news corespondents covering the war with Iraq are bridling under a system of conflicting rules and confusing censorship.

For the first time since World War II, correspondents must submit to near-total military supervision of their work.

The men and women covering the war are permitted to see and hear a great deal as members of pools who are given access to military sites. But they may not use place names or other clues that could help the Iraqis. Most accept such constraints without protest, but there have been instances when information that correspondents were ordered to withhold was made available soon after by officers in Washington.

This reporter encountered a telling example of the paradoxical censorship rules in a pool assignment last week, when officers on the scene said American forces had destroyed laboratories where the Iraqis were thought to be developing a nuclear potential. Best News From the Top

Permission to report the attacks -- a major development -- was denied by the unit commander, who said the information could assist Iraqi intelligence operations and should be witheld. Correspondents complied, but the information was later reported in detail by the American military commanders during their daily briefing in Saudi Arabia. The Pentagon is clearly eager to be the first to report the most newsworthy information.

Seemingly haphazard application of censorship rules has blanked out or truncated the timely release of some important articles even after they survived the required military "security review." In other cases, information deemed dangerous to American troops by commanders in the field has been cleared by the Pentagon and published or broadcast.

Most journalists here agree that military information officers at the Joint Information Bureau in Dhahran are helpful and fair. Many of the problems correspondents face originate in Washington, they say.

About 60 pool reporters selected from several hundred men and women covering the Persian Gulf campaign must share their dispatches and video and radio tapes with all their colleagues. The pool reporters go out in small groups, usually six reporters and camera operators, to some American unit on land or shipboard to observe activity. But the service men and women selected for interviews by pool members are chosen by information officers accompanying each pool, in cooperation with the unit commander. Appeal Process Over Release

In principle, every article or videotape prepared by a pool reporter is subject to a one-time censorship procedure in the field, which is conducted by the information officer in consultation with the unit commander.

If a reporter challenges any suggested changes or elisions, the challenge can be adjudicated by the Pentagon and the reporter's editors. In principle, even if the Pentagon rules against publicizing an event, information officers can only appeal to publishers and news directors to suppress it.

The rules can work against print journalism while benefitting television and radio broadcasters. While print journalists must submit written texts of their dispatches to field information officers and commanders for "security review," radio and television reporters often brodcast live without texts, permitting them greater latitude. Television tape, in eight-millimeter format, cannot be reviewed by the videocassette recorder equipment available to information officers in the field.

Varying interpretations of the rules imposed by the Pentagon have virtually blanked out timely publication of some articles that had been cleared by local commanders.

A pool dispatch prepared by The New York Times reported that F-117A radar-evading Stealth bombers launched the war against Iraq with precise laser-guided bombs that destroyed key targets in Baghdad. Second Thoughts by Commander

An Army public information officer cleared the dispatch on the spot for transmission to pool headquarters in Dhahran and then to news organizations themselves.

But more than three hours later, the unit commander had second thoughts about the dispatch, striking out a paragraph and changing words and phrases in others.

To hasten the transmission of the news, The Times reporter agreed to the proposed changes so that American publications and news services could receive it in time for deadlines.

The next day, however, the reporter learned that the entire article had been supressed by the F-117A unit headquarters in the United States. More than a day after it was written, when it had become stale news, the dispatch was cleared in its original form.

Most reporters are uncomfortable with a news system so completely under military control. The system implemented here has its roots in military dissatisfaction with news coverage of the Vietnam War, which some military officials continue to argue was lost by the news media.

A senior Air Force officer opened his briefing here last week by telling an auditorium filled with reporters: "Let me say up front that I don't like the press. Your presence here can't possibly do me any good, and it can hurt me and my people."