The red, white and green flag snapping smartly in a brisk breeze over a gracious mansion along the Tigris River looks ordinary enough among those of scores of other embassies in central Baghdad. That is, considering it is the flag of the Islamic Republic of Iran.

Inside the mansion, behind a formidable stone wall and a screen of inconspicuous security men, 15 diplomats representing a nation committed to the destruction of the "satanic" Iraqi government go about their business almost as if nothing were amiss.

It is one of the curious anomalies of the nine-week-old Iraqi-Iranian war that the two countries -- although gripped in a life-and-death struggle in the salt marshes around Abadan and the approaches to Ahwaz -- have never gotten around to declaring war on each other, or even breaking off relations.

"Why should they? Breaking relations is an expression of displeasure, and when you are at war, it seems a little redundant," observed an Asian diplomat whose government is friendly to both Iran and Iraq. "Besides, this is the Middle East," he said.

In fact, there is a practical economic reason why war has not been formally declared, diplomatic observers said. With a declaration of war, foreign contractors holding billions of dollars of contracts could assert force majeure and demand compensation.

Instead, Iraq's declaration of Sept. 22, when full-scale hostilities broke out and Iraqi and Iranian warplanes began bombing each other's cities, was very carefully worded, saying that Iran's actions amounted to war and that Iraq would respond militarily.

Although scaled back somewhat, Iran's embassy here is nearly a full-fledged mission, headed by a charge d'affaires who already was the top official at the start of the war.

An Iraqi security agent watching the main entrance from his car yesterday prevented correspondents from entering the embassy grounds and, after contacting his headquarters by radio, said that permission would not be granted.

Only three Iranian diplomats with families living elsewhere in Baghdad are allowed off the grounds, he said, and they are followed on their occasional home visits to prevent sabotage or subversive activities.

The agent said there have been no attempts by Iraqis to attack or vandalize the Iranian building. In addition to plainclothed agents, the grounds are patrolled by uniformed Iraqi soldiers carrying Kalashnikov assault rifles.

Nationalistic posters calling for an Iraqi victory have been pasted to a steel gate of one entrance on a quiet residential street, which runs along the Tigris River. It is over the Tigris where Iranian Phantom jets have swooped low on their way to bomb the nearby Dora oil refinery storage depot and a power station just upriver.

The embassy is said to maintain telex and telephone communications with Tehran, although diplomatic sources said they doubted whether the embassy staff -- virtually under house arrest -- would have very much to report to their Foreign Ministry.

The sources said they also had no indication that Iraq and Iran have conducted much of a dialogue through the mission since the days just before the war, when several ultimatums were passed back and forth.

Making the wartime Iranian representation here even more bewildering is the fact that Iran's ambassador, a Shiite mullah and top lieutenant of Ayatollah Ruhollah Khomeini when Khomeini lived in Iraq in exile for 15 years, was expelled last April for allegedly subversive activities.

The ambassador, Mahmoud Duwahi, reportedly was connected with the clandestine Shiite Moslem resistance organization, Al Dowa. He returned to Tehran and announced that the Iraqi people paid their respects to Khomeini.

This statement outraged Iraqi President Saddam Hussein, and was one of the early provocations that led to an explosion of tensions between the two countries.

The Iranian Embassy is just one of the oddities of what in some ways is a gentlemanly war -- almost chivalrous in a medieval sense despite the destructiveness of its 20th century weapons.

In the fierce battle for the port town of Khorramshahr, the Iraqi Army silenced its guns long enough for women and children to leave, a gesture that allowed the Iranians to infiltrate Revolutionary Guards into the city to take up sniper positions and establish pockets of resistance.Reports of atrocities have been rare, considering the bitter ideological nature of the war, and both sides have respected an unspoken agreement not to attack mosques in the other's territory.

When Iraqi security forces earlier this year raided the Syrian Embassy here and uncovered a large cache of weapons allegedly stockpiled for guerilla activities, the entire Syrian mission was immediately expelled. But now, diplomatic sources said, the Syrians are back in place and are routinely issuing visas -- even though Syria is tacitly supporting Iran in the Persian Gulf war.