The 19 Americans who died in the explosion in Dhahran, and the hundreds more who suffered injuries, were pulling tough duty to protect Saudi Arabia. The royal House of Saud needs an American shield. Its vast oil wealth has not bought security from the vengeance of Iraq’s Saddam Hussein or the machinations of Iran’s ayatollahs and their friends. And although they preside over one of the world’s most rigidly fundamentalist states, the high-living royals are denounced as hypocrites by ultramilitant Muslims. At any given moment, about 5,000 American military men and women are rotating through Saudi Arabia for 90 days at a time. More than 20,000 others stand guard elsewhere in the region (chart). For Saudis, the American presence is a painful paradox: they know they have to have it, but they resent the intrusion and are shamed by the need. And now, for the second time since five U.S. servicemen died in a bombing last November, Americans have become the target of what appears to be a homegrown conspiracy against the royal family.

The day after the explosion, Clinton and his advisers considered a quick presidential visit to Saudi Arabia. The discussion continued during the flight to France for the summit of the G-7 industrial democracies. Clinton said he wanted to be sure a visit wouldn’t interfere with the investigation of the blast. Finally, he and his staff decided to attend memorial services for the victims in Florida over the weekend, rather than descend on a country that already had more than enough on its hands.

Even without the irritant of an American presence, the Saudi regime would be in difficulty. For the first time in decades, economic problems have made many Saudis feel poor, and the air of discontent has never been stronger. Oil prices are relatively soft, and the war against Iraq imposed a crushing financial burden on the kingdom – as much as $120 billion. Thousands of recent university graduates are unemployed, and per-capita income has dropped from $14,000 a year in 1982 to $6,700 today. The economy is beginning to recover, but the country’s gold-plated welfare system has run out of cash. Hospitals in Riyadh now ask surgical patients to bring their own catheter tubes, which the hospitals cannot afford to buy.

The government preaches austerity, but that doesn’t seem to apply to members of the royal family, now thought to number about 15,000. The royals receive monthly stipends and free utilities and air travel and are accused of dipping into the national treasury as though it were their private bank. The fecund House of Saud may be draining off as much as 5 to 8 percent of the country’s $140 billion-a-year gross domestic product. ““They are asking us to tighten our belts,’’ complains a businessman in Riyadh. ““Why don’t they wear a belt?''

Along with everything else, Saudis have had to face questions about King Fahd’s ability to govern. After a crippling stroke last year, the king, now 73, dropped out of view, handing the reins of power to his half-brother, Crown Prince Abdullah. Then, in a whirl of family intrigue, he took them back. But he may not be up to the job, due to a failing memory. Diplomats say he recently forgot he had appointed a new ambassador to Egypt – then exploded in a rage when he heard the post was filled.

Accompanying Secretary of State Warren Christopher on a tour of the bomb site, Prince Bandar tried to be upbeat. ““We will catch the guys who did this,’’ he said, ““and when we do, I promise you it won’t be a trial like that of O. J. Simpson.’’ By the end of last week, the two men seen running away from the truck still hadn’t been caught. A senior Saudi official said investigators ““saw only three possible scenarios’’ for the bombing: ““It could be something like the November bomb. Or Iran, or Iraq.''

Most investigators leaned toward the first scenario; the bombing in Dhahran was carried out in a manner strikingly similar to the earlier one. Four young men, all Saudi citizens, were arrested for that bombing. They confessed, evidently under torture, and were quickly beheaded. The confessions, which were suspiciously similar to each other, said the men were inspired by Saudi dissidents living in exile and revealed that three of them had fought with the anti-Soviet mujahedin in Afghanistan. The confessions also tied them to Mohammed Maqdisi, a Palestinian who grew up in Kuwait and served in Afghanistan. Maqdisi, whose real name is said to be Issam Mohammed Taher, is now in a Jordanian jail. Sources there link him to a fundamentalist Saudi group called Biyat Al Imam. ““The danger of this organization is that it is not organized,’’ says Yasser Abu Hillaleh, a Jordanian journalist who has reported on the group. ““There is no leadership to speak of; they are impulsive.''

So far, the terrorists seem to represent only a few Saudis, and the regime will bring the full weight of the state against them. ““This is not Iran in the ’70s,’’ says a senior U.S. official. He points out that there are no large-scale demonstrations in Saudi Arabia and no charismatic leaders in exile. The monarchy still has the will to govern, and it still has strong middle-class support. But Saudi Arabia is a far more reclusive and mysterious nation than Iran was under the shah. Rebellions may be brewing out in the desert that foreigners haven’t even heard of yet. It’s impossible to predict whether the royal family will be able to handle the challenge indefinitely. And if the House of Saud ultimately loses its grip, the United States also may find it hard to hang on in one of the world’s most vital regions.