At the time, the bankers, appalled at the prospect of breaching their century-long tradition of secrecy, resisted. They publicly insisted that there were few such accounts and that any surviving heirs would know who they were and make claims.

When the bankers finally relented this week and published the list in newspapers around the world, Ambassador Kunin settled into a comfortable chair in her office at the American Embassy and scanned the columns listing about 1,800 names. One name leapt out of the tiny type: her mother's.

''There it was,'' she said today by telephone, her dog barking in the background. '' 'May, Renee, New York.' I was shocked. My mother died in 1970, and my brother and I were never aware that she left any money in Switzerland.''

Ms. Kunin, whose German Jewish family fled Switzerland in 1940 for fear that the Nazis would soon invade, has just begun the process of filing a claim to determine whether the Renee May on the list is in fact her mother. She has no idea how much is in the account.

But there is little doubt that her discovery -- that the Swiss bankers were directly negotiating with someone who might be one of the heirs they had insisted for half a century could not be found -- was one of the more unusual developments in a week of surprises.

And for the woman who has gone from wartime refugee to Governor of Vermont to Ambassador, it was a reminder of a series of anguishing childhood events: her father's suicide; a tense trip across the Italian border to the ship that would carry her to New York; cousins and other family members who stayed behind, thinking they were safe, only to perish at Dachau and other camps.

It also brought home the political complexities of pressing a reluctant and increasingly resentful Switzerland to unlock even more wartime mysteries buried in the country's vaults. It is a confrontation that is clearly making Ms. Kunin's superiors at the State Department nervous, and one in which many of the main participants, who now include the Ambassador herself, hold a very personal stake.

Today, not losing her diplomatic poise, Ms. Kunin preceded an account of her discovery with praise for the Swiss bankers' decision to publish the list, saying, ''I know that many families in need will benefit from this.''

''It took time, and it is too bad that it took so much time,'' she said. ''But it proves that once you publish a list like this, you get results.''

The main result so far has been the beginning of scores of minor mysteries. Like others who found family names on the list of accounts -- a former Harvard professor, a German pensioner living in London, the son of a Dutch diplomat -- Ms. Kunin has been searching her memory for any long-buried hints that relatives might have salted money away in Swiss banks.

Like most of the others, she is coming up with more questions than answers.

''She was not a woman of means,'' Ms. Kunin said today of her mother, who was born in Germany. ''My father had been in the shoe business, and he was a successful businessman.'' Although her father left her mother with a small inheritance, Ms. Kunin does not know how much her mother had by the time the family fled. ''She had been a widow for some time,'' she said.

At the time, Madeleine Kunin was just shy of 7 years old, and in her autobiography, ''Living a Political Life,'' (Alfred A. Knopf, 1994), she refers to her mother's ''inner turmoil'' in the years leading up to their flight.

Her father, Ferdinand May, drowned himself in a lake near Zurich after battling depression. A few years ago, in her first pass at exploring her family's history in Switzerland, Ms. Kunin obtained the medical reports from his stay at a psychiatric clinic. As she began to read them, she recounted in the autobiography, she finally understood the pain her mother had suffered.

''I cannot read the rest without crying,'' she wrote in the autobiography.

Her mother moved the family to a small town on Lake Lucerne, she wrote, believing that they would be safer in the countryside if Hitler invaded Switzerland.

At the same time, Ms. Kunin's mother was trying to get a visa to the United States. A Swiss bank, Banque Federale, wrote a reference testifying that her mother had ''sufficient means'' to support herself in America. It is unclear whether the account that led to that letter is the one uncovered on Wednesday.

Her wartime experience, Ms. Kunin wrote, led to her political career. ''On some level that I do not yet fully understand,'' she wrote, ''I believe I transformed my sense of the Holocaust into personal political activism. This was the source of my political courage. I could do what the victims could not: oppose evil whenever I recognized it.''

But what the bankers' lists have shown this week is nothing so simple as good and evil. The account holders include victims, victimizers and odd bystanders, a reflection of the Swiss policy of neutrality that assured that the banks dealt with all sides, taking in Jewish assets but also dealing in gold looted by the Nazis.

Untangling that history five decades later has engulfed the Ambassador in a diplomatic squall whose winds seem to increase with every new development.

It began with the hearings last year sponsored by Sen. Alfonse M. D'Amato, the New York Republican. The disclosures at those hearings -- particularly the testimony of Holocaust victims who hit a brick wall when they sought to enlist the banks in finding accounts that they believed their families had opened -- led to mounting criticism.

The banks agreed to an independent audit, led by Paul A. Volcker, the former Federal Reserve chairman. A comprehensive study published in April by the Clinton Administration concluded that the banks had aided the Nazis, stiff-armed the Holocaust survivors and hidden assets, now worth billions, that they agreed in 1946 to turn over to the Allies.

In Switzerland, the reaction has been intense. Politicians, diplomats and commentators accuse the United States of acting imperiously. The bankers have defended their actions during the war but deflected questions about what their institutions did after the German surrender, when the country was no longer at risk of being overrun.

In recent months, State Department officials have sought to tone down the criticisms of Switzerland, causing sharp divisions in the Administration. Some diplomats warn of the dangers of a major breach with Switzerland when it is beginning to help track down international drug dealers and money launderers.

Ms. Kunin is on the front line, trying to press for more disclosure without fanning the flames of resentment. Already, polls show that a national referendum to establish a charitable fund, the Swiss Government's main response to the international pressure, could be headed for defeat.

Photo: Ambassador Madeleine Kunin says she was ''shocked'' to find her mother's name on a list of dormant Swiss bank accounts. (Associated Press)