With a fine sliver of a crescent moon etched over the blue-doomed Mashad Ali mosque in this holy city south of Babylon, the muezzin's call to evening prayer floated through streets so bustling and brightly lit as to seem oblivious of the war Iraq is waging with neighboring Iran.

Where elsewhere in the land the muezzin's chant in the evening is taken as a signal for lights to be turned off, blinds drawn and business to wind down as the nighttime blackout of war sets in, here in Najaf the traditional Arab street life does not miss a beat.

There is good reason for the nonchalance about the war here. For Najif is one of the holiest shrines of the Moslem Shiite sect, which is the religion of the ayatollahs of Iran as well as about 60 percent of the people of Iraq. Supposedly under the grand mosque, with its flanking four minarets, is the burial site of Ali, cousin and brother-in-law of the prophet Mohammad, the founder and the first imam of the Shiite sect.

For the mullahs of Iran to choose to bomb targets around Najaf would be sacriliege or, in the terms of their Islamic penal code, "corruption on earth" and "warring against God."

But Najaf also poses serious problems for the Iraqi government of President Saddam Hussein.

"If there ever is a violent outbreak against the government, this is where it will begin," one foreign-educated Iranian here said.

With Army patrols checking the crowds passing through the hastily fenced-off mosques of the city these days and secret police officers at every teahouse, hostel, retaurant and street corner, the people of Najaf are reticent about talking to strangers. In the midst of the war, however, they are not demonstrating in the streets, either.

But the blase way the devout Shiites of Najaf go about their business, showing outright contempt for the war precautions elsewhere in the land, is a sign of their particular protest against the war:

The city's devout Shiism, unlike elsewhere in Iraq has left it highly suspect in the eyes of Baghdad authorities who suspect it of being a bastion of Shiite fifth columnists against the Iraqi government.

It was here that Iran's Ayatollah Ruhollah Khomeini came to settle in exile in 1964 after the shah of Iran expelled him for his opposition to the shah's much ballyhooed "white revolution," one of whose key tenets was the expropriation of the vast church landholdings on which Iran's mullahs base their power in the countryside.

For 14 years Khomeini lived here, in a small unpretentious, one-story house, while teaching at a Shiite theological seminary. Here he first gathered around him the mullahs, Shiite seminarians and young anti-shah university students who played such a decisive role in Iran's Islamic revolution two years ago.

It was here, too, that Khomeini first developed and articulated his vague, mystical, and messianic dogma of Islamic revolution, a revolution which, in his terms, has no national boundaries and is as applicable to Iran as to Iraq and other nations along the strategic Persian Gulf where there are significant numbers of Shiites.

The ayatollah's insistence on proselytizing his Islamic revolution not only among Iranians but also among the devout Iraqi Shiites who troop to Najaf in pilgrimage every year, put him on a collision course with the Iraqi government ruled as it is by a tightly knit clan of minority Sunni Moslems who control the ruling Baath Arab Socialist Party.

Saddam Hussein, at the time the government's hatchet man, ordered Khomeini to keep his politics to himself. When the ayatollah refused, Saddam Hussein unceremoniously expelled him in 1978, earning his undying hatred.

No sooner had Kohmeini succeeded in toppling the shah, than he launched a vitriolic campaign to stir up the Iraqi Shiite majority against his old antagonist Saddam Hussein, who in the interim had become the president of Iraq.

"The time has come to overthrow Saddam's godless regime and to free the Iraqi Moslem people from his oppressiveness and tyrany," Khomeini said in one recent radio broadcast from Tehran that set the tone of his diatribe against his enemy. Saddam Hussein has replied in kind, calling Khomeini a "charlatan" and a "tyrant" and much worse.

Such violent exchange of personal insults made the war Iraq launched against Iran on Sept. 22 virtually inevitable.

With his own government a narrowly based minority regime dependent on family and clan ties at the top and rigid police state authoritarianism at the bottom, Saddam Hussein was vulnerable to Khomeini's public ridicule and incitement of the Shiites of Iraq.

To undercut the threat they posed, last spring Saddam Hussein simply expelled about 20,000 of the most suspect, primarily Iranian-born Iraqis, who were taken to the Iranian border and herded across it. In April he ordered the arrest and summary executions of the most militant of Iraq's three Shiite ayatollahs, Mohammed Bagher-Sadr. It was an act calculated to stir the anger of the faithful here in Najaf where demonstrations against the government simmered until the Army and secret police garrisoned the town.

"Today there are almost as many secret police in Najaf as there are local residents," said one disgruntled foreign-educated company official. "The city is the regime's Achilles heel."