His Serene Highness Hans Adam, heir to the last state of the Holy Roman Empire, arrived from the airport last week in a taxi. The few but fanatical lovers of the Principality of Liechtenstein were disappointed. They had hoped the prinz would ride down Fifth Avenue in the rococo Golden Carriage in which his ancestor made his ceremonial entry into Paris on Dec. 21, 1738.

The present Prince Hans Adam would look every inch like Ronald Colman in "The Prisoner of Zenda," had he but an ermine robe, a lance in his hand and the crown of Liechtenstein, which unfortunately was misplaced.

But on this day, in his new New York financial offices in the Seagram Building, wearing a dark striped suit, he looks like any other nice man, a young 40, just gray enough to seem financially reliable. He poses for the photographer before a photomural of the Vaduz (Liechtenstein) castle. His publicist stops the camera to tell the prince to pull up the royal socks. He does so, dutifully.

Even so, the prince's triumphant entry had the most elaborate accouterments of any royal visitor anywhere. For two months before the Erb (crown or hereditary) Prinz von und zu Liechtenstein himself arrived, he was preceded by 16 plane-loads of rare riches: 19 paintings by Peter Paul Rubens, five by Anthony Van Dyck, Baroque and Renaissance sculpture, ivory carvings and porcelains and other paintings by Austrian, Dutch, Flemish and Florentine old masters -- all protected by the world's largest collection of 16th- to 18th-century decorated firearms.

The 3,100-pound Golden Carriage, decorated with paintings by the studio of Francois Boucher, was dismantled and reassembled as it had been in 1760 when Prinz Joseph Wenzel von und zu Liechtenstein traveled over the Alps to Parma.

The 218 artworks, none before seen outside Europe, will be exhibited in the Metropolitan Museum of Art Oct. 26 through May 1, 1986 following a month of member previews that began this week and last night's exclusive dinner there.

It's not a bad collection for a country roughly the size of the District of Columbia (60 square miles), with a population comparable in number to that of College Park, tucked Shangri-La-like into a Rhine valley by the Grauspitz Mountains between Austria and Switzerland. With its low income tax and high per-capita income ($20,000), Liechtenstein has more corporations (30,000) than people (26,000), and is better known for its postage stamps than for a leading industry -- false teeth.

Yet even with its major treasures on tour here, the family's three palaces and three castles in Liechtenstein and Austria are not bereft of artworks. The bulk of the collection is kept in a tower in Vaduz Castle. The recent acquisitions are shown in the village of Vaduz and plans are under way for an art gallery.

Prince Hans Adam, in an ordinary office, with not a hint of gold leaf, doesn't stand on ceremony. He sits down with an open and easy air, prepared to answer anything. His English is fluent, with only enough German accent to sound right in the role of the prince, whose country inspired dozens of mythical kingdom books and movies.

The Liechtenstein fortune and art collection are said to be second only to the royal house of Windsor. Says Hans Adam: "I think they are stronger in some fields of art. We are stronger in others. Theirs is larger or more valuable. But it's always very difficult to say. I'm not expert enough to judge."

With all these trappings of wealth and position, Hans Adam is steadfastly in favor of the quiet life, living with his four children in two floors of Vaduz Castle, facing the mountain, and only a few times a year giving a great ball in one of his Viennese palaces. More and more his parents, the Fu rst Franz Josef II and the Fu rstin Georgine, spend their time in a hunting lodge further up the mountain.

"Liechtenstein is a marvelous place to grow up. Our children can lead a very normal life, a country life." They play tennis, soccer and lacrosse and they ski in the winter.

"When I married my wife, we decided to bring up our children ourselves, like a normal family. I thought it would be good to devote a lot of time to that. In a monarchy, your successor is already fixed. You can do a fantastic job, but if your successor is no good, then in the long run, it doesn't make sense."

Hans Adam was not brought up so simply. He did go to school in Vaduz, as his three sons (17, 16 and 13) and daughter (12) do, but "had to finish school in Austria and Switzerland. At 18 he spent two months in Washington, working for Sen. Claiborne Pell (D-R.I.).

Hans Adam, whose father studied forestry, majored in economics.

"My father," he said, "was brought up with private teaching. It would have been a bigger change for them to bring us up by themselves. So we had nannies and teachers to look after us."

But if life then, as now, was determinedly secure, it hasn't always been. For 700 or so years, the ruler of Liechtenstein had a "principality on the Rhine and a kingdom in Bohemia" and in the 17th century ruled a half-million people or more in Moravia. Even today, the Liechtenstein acreage in Austria is larger than the principality itself.

Prince Hans Adam is named after his ancestor Johann Adam (1657-1712), called "Hans the Rich," who bought the two Upper Rhine counties of Schellenberg in 1699 and Vaduz in 1712 to establish the country and gain a seat in the Holy Roman Empire. Legend has it that the previous owner kept losing the country at cards.

The House of Liechtenstein lost 85 percent of its wealth during World War II, including 54 castles outside its borders, though the country itself remained neutral in the conflict. In 1967, Hans Adam's father, the Fu rst of Liechtenstein, sold Leonardo da Vinci's "Ginevra de 'Benci" to the National Gallery of Art for $5 million to put the family back in business. Now Hans Adam's collections director, Reinhold Baumstark, is combing the auction houses of the world to buy back works of art the family sold in less prosperous times -- and a few more.

Before World War I, Liechtenstein was bound by treaty to Austria, where the family had been second only to the Hapsburgs in military and financial power. In the '20s, Liechtenstein citizens gained a constitution and in 1938, on the eve of World War II, Franz Josef, then 32, moved from the family's great palaces in Vienna to Vaduz -- the first of his line to actually live in their country.

During World War II, Franz Josef courted his wife, Georgine von Wilczek of Czechoslovakia, in a farm work camp where she had been confined. Some years ago, she remembered that instead of jewels, he brought her Swiss chocolates, a rare gift during that era. They were married in 1943.

Just as World War II was winding down, Franz Josef heard that the Soviets were moving toward the salt mines of western Austria where 1,700 works of art had been moved from the great Viennese palaces for safekeeping. Hitler had given orders the salt mines were to be blown up before the Soviets reached them. Through a member of the Liechtenstein family, he obtained a permit from Nazi Minister of Culture Joseph Goebbels to remove paintings of "members of the Liechtenstein family and officers of the Liechtenstein government."

"The size of our family increased tremendously," Hans Adam said with a knowing smile. Among the hundreds smuggled out were a series by Rubens described by one critic as being "without parallel in any museum in the United States."

Though his permit was good for only one trip, Franz Josef's aide crisscrossed the border several times to rescue the art. The mines were full of other treasures of the Austro-Hungarian Empire. "We could have had the crown of St. Stephens, if we'd wanted it," Franz Josef said years later.

Liechtenstein could have used it. Its own crown hasn't been around since the 18th century. "We don't really know what happened to it," said Hans Adam apologetically. "I suppose one of the ancestors thought it wasn't interesting anymore to have a crown. Perhaps he had a wife who thought to make some nice jewelry out of it."

During World War II, Hans Adam said, "Some things left back in the palaces in Vienna and the castles in Czechoslovakia were destroyed. The Soviet soldiers liked to carry the furniture to the top floor and throw it out the window so they could see it go in a thousand pieces. There was also some shooting of beautiful pictures on the walls."

Hans Adam today credits his father, now 79, for "keeping us out of World War II. It was very close that we were not occupied by the Third Reich. Hitler had hoped we would join the Third Reich voluntarily by Anschluss. But our people would not agree. Those few who liked the Third Reich were put over the border into Germany since they preferred it."

When Franz Josef and Gina set up housekeeping in the Vaduz castle, then hardly habitable, they were almost overwhelmed by refugees from Nazi reign in Austria and Germany. Among them was a distant relation, the then Grafin (Countess) Marie Aglae Kinsky von Wehinitz und Tettau, who'd been born in Prague. Later, when Hans Adam was 17 and on holiday, they met. He went directly to the schloss and told his father he wanted to marry her. "My parents were very surprised. They made us wait for five years."

Not just Hans Adam, but all the 100 members of the Liechtenstein family still have to ask the Fu rst for permission to marry.

Most of the Liechtensteins lost all they had in World War II, and, as Hans Adams put it, "we had to recreate them" financially.

Franz Josef, with proceeds from the 1967 sale of the Leonardo to the Met, went to work rebuilding the Liechtenstein finances. And a few years later, at 25, Hans Adam reorganized the family fortune into the Prince of Liechtenstein Foundation.

Franz Josef, who has ruled longer than any other currently reigning monarch, in 1980 made his son "more or less the head of state."

The Metropolitan Show is only one example of the Liechtenstein family's success in regaining the position it wielded before Franz Joseph's uncle, Franz Ferdinand, was assassinated at Sarajevo in the event that triggered World War I.

Their present visibility no doubt comes because the Prince of Liechtenstein Foundation, a holding company, now owns 50,000 acres of forest and 20,000 acres of urban land in Austria, not to mention 100,000 acres in Texas. Its bank, with subsidiaries in Frankfurt, London, Zurich, and New York, has a balance sheet near $2 billion, two venture capital companies and, among other things, a theatrical publishing house in Munich.

Hans Adam, who would have been a natural scientist if he had not been the oldest of the five children, is interested now in international politics. His great scheme is to join Liechtenstein to the United Nations.

"Now we have to look outside Europe. I think the U.N. would be the most sensible step. We have the possibility to have relations with many, many countries. We are too small to have embassies all over the world. But on the economic side, over 30 percent of our exports go outside Europe."

Hans Adam has a small problem -- the citizens of Liechtenstein. It took three elections before they agreed with him that women should have the vote. He's yet to convince them on U.N. membership.

And why have the Liechtensteins been so favored with fortune and felicity? Hans Adam thought a minute. They've been flexible, he said.

As he left to go back to the Pierre Hotel, one of his aides said, "It doesn't seem right to let him walk down the street unescorted." The other replied: "He likes it that way."