THERE was a time - not too many years back - when Pan American World Airways was a shining symbol of United States economic and aviation prowess.Pan Am planes, from the famed flying boats of the 1930s to the Boeing 747s of the jet age, roamed the air corridors of Europe, Latin America, and parts of Asia. And always winging along in the distance in recent years was Pan Am's main US rival: Trans World Airlines. Taken together, Pan Am and TWA were the royal family of US international air travel - its flagship airlines. Today the ruling family finds itself in deep trouble. Pan Am is in bankruptcy court. TWA, although not in bankruptcy, has substantial financial liabilities. Clearly, US air leadership is passing to a small group of carriers - American Airlines, United, Delta and Northwest. "Those four carriers will likely dominate the [US] industry throughout the 1990s," says Earl Gaskins, who follows the airline industry for Provident Capital Management Inc. in Philadelphia. Because there are so few carriers involved, says Mr. Gaskins, the dominant survivors can be likened to an "oligarchy." Geoffrey Dann, an analyst with Smith Barney, Harris Upham & Co., sees the same big four and possibly a fifth major player: Continental, which has an extensive route structure. Eastern Airlines, which used to announce proudly that it carried more passengers than any other airline "in the free world," has disappeared into bankruptcy. "The airlines that survive into the next century will be companies that have strong international operations as well as strength in the domestic US market," Gaskins says. "Load factors are higher on overseas routes than US runs," which means that overseas planes are more economically utilized. In addition, passenger growth is expected to be faster abroad than in the US. Overseas revenue growth is also expected to climb faster than in the US market. Financially strapped Pan Am now faces outright dismantling, underscored by the new bargaining this week for the carrier. TWA, in a linkup with American Airlines, has offered to pay $450 million to buy Pan Am. Under the complex deal, TWA would sell off Pan Am's routes to Italy, Spain, and Portugal (plus the domestic Pan Am Shuttle), to American Airlines for $250 million. Earlier, Delta Air Lines offered $260 million for various Pan Am assets. Finally, United Airlines has reportedly boosted its offer for Pan Am's Latin American routes, and is said to be preparing a joint bid with Delta to compete with the TWA/American offer. Any sale of Pan Am assets would have to be approved by the bankruptcy court as well as federal regulators. The Pension Benefit Guaranty Corporation, a federal agency that insures private pension plans, moved Wednesday to take over two Pan Am plans that were underfunded. The agency says its step should facilitate the sale of Pan Am assets. But whatever happens regarding assets now held by Pan Am, the current shakeout in the US airline industry is expected to produce far-reaching change: * Size will become increasingly important to US carriers, experts say, as overseas airlines step up their competition on key international routes. The result may be additional mergers during the next few years. * Airlines with primarily domestic routes will be at a financial disadvantage against carriers with strong overseas routes. * More jobs will be lost - including many at Pan Am. * Industry consolidation may push fares higher, analysts say. * "Niche carriers" that are in strong regional markets, such as Alaska Air on the West Coast or Southwest in Texas, can be expected to thrive as they build customer loyalty. The industry in general, experts note, has been hard hit by the recent recession. Nor would a modest recovery give the larger carriers the travel kick now needed to bolster their ledgers. Indeed, first-quarter losses for the major carriers in 1991 were "worse than expected," writes airline analyst Daniel Hersh in a recent study for Kemper Securities Group Inc. He sees the less-than-upbeat scenario continuing into the third quarter of 1991. Mr. Hersh notes that while revenue has faltered because of recession, unit costs, excluding fuel, have been growing equal to or higher than the rate of inflation. That stems from high wage settlements, plus higher facility costs in some areas.