The new president of Iran, Abol Hassan Bani-Sadr, had just put his finger on a clear and present danger that could in the end, create more difficulties for the United States than the threat of Soviet military aggression in the area.

With attention focused on what Bani-Sadr had to say at his inauguration about the American hostages, little notice was paid to his quite, but ominous warning that "our revolution will not win unless it is exported." And he added: "We are going to create a new world order in which deprived people will not always be deprived, and oppressors will not always be oppressors."

He made it plain that he was talking about "destroying the remains of monarchy." Those are alarming words to the dynastic rulers of the Arabian Peninsula, for that oil-rich zone is the world's last stronghold of absolute monarchs, who still reign as if 1980 were in the Middle Ages.

It is not surprising that the sultans, sheiks and kings, who have become the wealthiest men on earth through petroleum, are already nervous about the shape of things to come, since what happened to the shah of Iran can also happen to them. It is a sound bet that, like dominoes, most of them will fall before the end of the century, if not much sooner. They are natural targets for revolution, insurrection and assorted coups.

And as Iran has shown, such a train of events would pose acute problems for the United States and affect our supply of oil, on which we now depend so much.

The biggest potential domino, of course, is Saudi Arabia, where the royal family was recently shocked by the seizure of the Grand Mosque in Mecca by hundreds of armed militants. Publicly, the government has tried to minimize it as an isolated event; but Egyptian President Anwar Sadat, like many others, believes it is a symptom of broader discontent.

In any case, the royal family, which numbers over 2,000 princes, has toughened the enforcement of strict Islamic laws, the security forces have been shaken up and now, as a democratic gesture, there is talk of forming an elected consultative council.

A growing threat to the dynasty is the large number of students and military officers who have been educated and trained abroad, where they have been exposed to radical and revolutionary ideas. The Middle East Intelligence Survey reports that there have been instances "in which members of the regular army were involved in attempted coups against the regime."

The rising tide of political instability throughout the region is, as Fortune reports, "aggravated by widespread corruption, extremes of wealth, and the presence of large numbers of Palestinians and other foreign workers."

Although many of the immigrant workers have been living in the Gulf countries for years, few enjoy the prerogatives of native-born citizens. These disgruntled people, Fortune finds, "are prime recruits for the dissident movements that abound in the Middle East."

Kuwait's aliens outnumber its native population by 2-to-1. Oman, which has a history of insurgency, has also encouraged the influx of foreign workers. The best proof that Oman is susceptible to coups is that the present sultan, Qabus bin Said, seized power in 1970 by overthrowing his own father.

In neighboring Yemen (both North and South), the leadership has changed in recent years through assassination and execution. On the other side of Oman is Bahrain, where the emir, a Sunni Moslem, reigns uneasily over a Shiite majority.

The upsurge in Shiite fundamentalism that marked the Iranian revolt is seen in the diplomatic world as a danger to governments in Pakistan and Turkey. Some observers also think that Iraq, at the head of the Gulf, may be tempted to poach on nearby oil fields.

Moreover, if Syria's withdrawal leads to a renewal of civil war in Lebanon, the whole region will be in turmoil. As the Middle East Intelligence Survey notes, there is "hardly a single undisputed border" in the Persian Gulf area.

What can Washington do to arrest the spreading political disorder in the region? Not much, it appears. But the situation ought to be compelling proof that, regardless of Soviet intentions, the national security of the United States requires a much more urgent effort to free the country from dependence on Arab oil, no matter what it demands in dollars and self-discipline.