Women reporters covering the U.S. military buildup in male-dominated Saudi Arabia exulted when the invitation came to join female soldiers in their exercise classes. Exclusive! We gloated. But the chance to swim and sweat with the U.S. women in uniform nearly backfired when the three reporters - myself included - walked through the front door of the $80 million gymnasium at a Saudi air base. Several Saudi custodians, all men, leapt up and followed us to the registration desk, complaining loudly that we had violated custom by using the front entrance. Women, they said, must enter through the rear door. Our timing, it appeared, couldn't have been worse: we had committed this faux pas on a Friday - Islam's holy day - during Moslem prayer time. The Saudis were not the only ones who were annoyed. `You nearly ruined it for all of us,'' one angry Air Force nurse told the sheepish reporters. ``They almost kicked us out.'' The military women had fought hard for the privilege of using the gym three times a week, and they dreaded the idea of losing it. The culture clash was an example of the hidden challenges that American women encountered in Saudi Arabia, a country where females don't vote, don't drive, don't go out in public without covering their faces and heads with veils, don't socialize in meeting places and rarely hold jobs that bring them in contact with the general public. Most Saudi women seem to accept the social structure that is based on the laws of Islam. They say they are put on a pedestal in their homes and treated generously by their men. The female reporters - writers, television and radio correspondents, photographers and television camera crews - have been treated fairly by both Saudi and American officials in terms of access to events and opportunities to cover the U.S.-led military deployment. We have slept on cots in the desert with the 82nd Airborne out of Fort Bragg, N.C. We have visited Egyptian paratroopers near the Saudi-Kuwaiti border; interviewed the powerful Saudi petroleum minister; and toured the strategic petroleum refinery at Ras Tanura. In deference to Saudi custom, we cover our arms, wear longer skirts and keep bare skin to a minimum. But none of us wear the black cloaks known as abayas or head coverings. The heat argues against wearing stockings. We act generally as we do in the United States: eating in restaurants, sipping coffee in the hotel lobbies. But we remain oddities on the social scene, the only women attending an Arabian nights dinner under a big tent hosted by Saudi prince, for example. We were warned about the muttawa, the so-called religious police who enforce the Islamic dress code and insist conservative standards are upheld. But an informal survey indicated none of the reporters has been accosted by the muttawa, who have the power to make arrests. On the streets or in the souks (markets), our small cadre of female reporters has grown accustomed to sares from curious Saudis, but the incredulous looks did not interfere with work. The major complaint - and the biggest frustration - is the ban on driving. We must hire taxis, drivers or rely on male colleagues to ferry us around, an expensive inconvenience in a country with a modern system of interstate highways. The U.S. Embassy also advised women not to sit next to a man to whom she was not married. In one case, I drove to a remote post on the Saudi-Kuwaiti border with a male colleague, 300 miles from the coastal city of Dhahran, to meet with the governor of the province. The trip would have been impossible without a male escort. Air travel was potentially a problem because Saudi custom dictates women must be accompanied by a male relative. Expatriate women have to obtain a letter approving their travel from their sponsoring company. Airports have check-in lines designated for ``males'' and ``families.'' Saudi officials seemed to ignore the rules for the foreign reporters. I was never asked about my marital status, for instance, when I flew to Riyadh, the Saudi capital, in the company of an American male reporter. Female reporters benefit from the famed Saudi hospitality and generosity. When one reporter mentioned she had lost a contact lens, her host insisted on having his driver take her the next day to the clinic for a replacement. At Prince Mohammed Bin Fahd's daily Majlis - a combination of a town meeting and a magistrate's court - Saudi citizens ask the governor of the Eastern Province to resolve problems ranging from land disputes to homelessness. After meeting the prince, I jokingly told himII had some problems he could solve. Pressed on what theywere, I assured him I was only kidding. That night, I received a call from the prince's worried press officer. ``You mentioned you had some problems and the prince wanted to know if there was anything he could do,'' the press officer said. ``A car to take you shopping? Some interviews? Anything?'' --- EDITOR'S NOTE - Joan Mower, a Washington reporter for The Associated Press, reported from Saudi Arabia for four weeks.