Last week's theft and quick recovery of 20 major Van Gogh paintings from a museum in Amsterdam left authorities puzzled as to who was responsible and why they abandoned their booty shortly after the robbery. But the incident also raised other questions that surface every time such a theft takes place.

Who would steal unique and world-famous paintings that would be difficult, if not impossible, to sell? How would they get rid of them? Is there some international ring that organizes major art thefts? What about security -- is it getting better?

In addition, the paintings taken last Sunday from the Van Gogh National Museum were not insured; do museums no longer insure their art?

And is theft from museums on the increase? Last Thursday, just four days after the Amsterdam incident, there was an attempted theft of a 19th century vase at the Walters Art Gallery here. A psychiatric outpatient was arrested after dropping and breaking the $5,000-$10,000 vase.

Constance Lowenthal, who heads a New York-based registry of stolen art, believes art is often stolen by people who then don't know what to do with it. "Many thieves who have turned to stealing art know very little about the art world," said the executive director of the International Foundation for Art Research, which keeps records of art thefts worldwide and disseminates information on those works. Rather than a master ring of international art thieves, she thinks perpetrators are often unsophisticated. "They know the headlines, they know how valuable [the art] is, but they don't know how to get rid of it. They learn the hard way that payday is not around the corner."

The FBI's national art theft coordinator, John Louden, said last week that he isn't aware of any master theft rings either. Nor, he added, is he aware of any "official underground organization that moves stolen art."

Ms. Lowenthal cited the 1988 Colnaghi theft as an example of lack of sophistication. Thieves entered the Colnaghi Art Gallery in New York and stole 28 old master paintings and drawings valued at $6 million. "The thieves had no prior idea of the value of what they were taking. When they saw [the figure] in the press they panicked and sold everything for $40,000 and left the country." Fourteen of the works were later recovered, she said.

In 1988, 145 items, including rare Oriental porcelains, were stolen from the Walters Art Gallery by a security guard and subsequently recovered. At the time of that theft, Ms. Lowenthal said that small, non-unique items such as porcelains are favored by thieves because they're easy to carry and often are "interchangeable and sort of anonymous." Such famous and unique works as the Van Goghs stolen in Amsterdam, or the paintings by Rembrandt, Vermeer, Degas and others stolen from the Gardner Museum in Boston last year and not yet recovered, are too well known to be sold through any legitimate channels.

But there are people who will receive such art, though usually for only a small fraction of what it's worth, she said last week. "Sometimes if they don't buy it they will accept it as partial payment in some other suspicious deal. It is after all a very valuable cash equivalent and one that travels across borders more readily than millions of dollars in cash. It's not too hard to cook up false invoices, and most customs people don't recognize things from a list of thousands of stolen items."

The difficulty of selling well-known stolen art may send it underground for years. Last year a group of paintings stolen in 1985 from the Marmottan Museum in Paris, including works by Renoir and Monet, turned up in Corsica. "From what I've read in news accounts," Mr. Louden said, "the thieves attempted to sell them on the illicit market and couldn't. They were stuck with them." He added that the FBI has recovered pieces "stolen 20 or 25 years ago."

Stolen art may "go to a fence fairly quickly, or get warehoused or abandoned" when thieves realize it's too hot to handle, Ms. Lowenthal said. And one of the best ways to make it too hot is to get the word out as fast as possible. As soon as it learns of a theft, IFAR notifies the art community (dealers, auction houses) immediately. And Interpol, which operates as a police communications link, notifies authorities in 154 countries.

But it's not easy to get stolen art back. Since IFAR began keeping records in 1976, about 35,000 objects have been reported to it as stolen. Only about 12 percent is recovered.

Knowing that stolen art will be hard to get rid of, thieves can take another course: ransoming it back to the people or institutions it was taken from. "At that point you have an 'artnapping' scenario," said Ms. Lowenthal. But the police are good at dealing with such scenarios, she said, and the thieves' strategy often proves unsuccessful.

While museum thefts of any scale usually make the newspapers, their number is "small" in "relation to home burglaries," Mr. Louden said.

In fact, says Robert Burke, director of security at the Smithsonian Institution in Washington and chairman of the American Association of Museums' security committee, museum theft has apparently been declining. He said the opening up of Iron Curtain countries has produced information that has not yet been analyzed in regard to thefts, but nonetheless there are "about 25 percent fewer incidents" of reported thefts from museums than 10 years ago. He emphasized, however, the term "reported thefts."

"I don't know, but I fear that [museums] don't always report all of their thefts," he said. "For insurance reasons -- if you report a theft, insurance may be higher. Another reason is status" -- people might be less inclined "to lend objects to museums that have reported thefts."

If museum theft has declined, better security systems may be a reason. Mr. Burke cited three major areas of improvement. First, "the technical equipment being used has undergone massive upgrading, from bells and whistles to computerization. Second, there has been a massive effort to improve training of personnel coming into the field, museum guards and museum staff. Third, there has been a major effort on the part of the American Association of Museums and the American Society for Industrial Security to educate the client community -- museums, archives, libraries -- in the need to upgrade their security and fire protection."

Still, he said, "a security system does no more than announce that something is happening, and calls for assistance." In the Amsterdam case, the thieves apparently hid in the building when it closed and later that night forced guards to turn off the alarm system.

That incident, like all such cases, will be studied to see what lessons can be learned, Mr. Burke said. In the Gardner Museum case, thieves dressed as policemen talked themselves into the museum at night. After that, "I doubt if anyone dressed in uniform could get into any museum at night," he said. "There is continual analysis and upgrading of procedures and alarms."

Partly because museum security is good, insurance costs have not risen dramatically with the astronomical rise in art prices over the past decade. "Rates have not only held but are decreasing," said Carl G. Allen, chairman emeritus of Allen Insurance Associates of Los Angeles, major brokers of art insurance. He would not be specific about how much rates have declined DTC because of differences in each museum's case.

What counteracts declining rates, however, is the increasing valuation of art. The Van Goghs taken in Amsterdam were reported uninsured because of increasing premiums. According to Mr. Allen, "In America there are very, very few [museums] that do not have [insurance]." But museums cannot insure more than a fraction of the total value of their collections, so they insure under the principal of "the probable maximum loss that could occur in any one foreseeable incident," Mr. Allen said.

Michael Fischman, vice president of Republic Hogg Robinson of New York, another art insurance broker, estimated that "95 percent of U.S. museums are insured" and agreed that they are "underinsured but underinsured intelligently."

In Baltimore, the Walters carries $100 million worth of insurance, and the Baltimore Museum of Art $150 million (recently increased from $100 million). According to Walters director Robert P. Bergman, who said "it is impossible to evaluate the total value of the Walters [collection]," the museum would probably be adequately covered, for instance, "if a plane crashes into a corner of the fourth floor." But $100 million would be "nothing" if for some reason the whole collection were destroyed.

The two museums' insurance is handled through the comptroller's office of the city of Baltimore. Douglas Pierson, assistant to the comptroller, works on insurance matters for the city and says that insurance premiums on the $100 million each museum had through last year remained "pretty much level" for "at least the last five years."

The cost of the BMA's $100 million worth of insurance was $105,000; the cost of $150 million is $120,000, he said. "Once you get above a certain point in insurance the likelihood of a loss in those dollars is less so the premium is less." The cost of the Walters' $100 million insurance is $75,000. The difference between its cost and the BMA's has to do in part with the greater number of traveling shows the latter presents, Mr. Pierson said.