The "tomb" stands dark and hulking at the heart of the Yale University campus, almost windowless, and shuttered and padlocked in the thick snow of winter storms.

Yale's candidates for the White House pictured in their student days and the 'Skull and Bones' mascot

Built to mimic a Greco-Egyptian temple, it is the headquarters of the Order of the Skull and Bones, America's most elite and elusive secret society - and it has become the unlikely focus of this year's presidential election. It turns out that four leading contestants for the White House in November's election were 1960s undergraduates at Yale: President Bush and Democratic rivals Governor Howard Dean, Sen John Kerry and Sen Joseph Lieberman.

What is more, two are "Bonesmen". Both Sen Kerry, now the Democrat front runner, and President Bush belong to the 172-year-old society, which aims to get its members into positions of power. This presidential election seems destined to become the first in history to pit one Skull and Bones member against another.

The phenomenon of the "Yalies", as Yale alumni are known, has provoked an intense debate over apparent elitism among Americans amazed that - in a democracy of almost 300 million people - the battle for power should be waged among candidates drawn from the 4,000 who graduated from Yale in four different years of the 1960s.

"To today's Yale undergraduates it seems quite extraordinary," said Jacob Leibenluft, a student and a reporter on the Yale Daily News, the campus newspaper. "For some it's a source of pride, to others it's a source of shame."

In fact Yale, with annual tuition fees of $28,400 (£16,000), has long sent graduates to the top of all professions from the campus in New Haven, Connecticut, where it was founded in 1731.

The Skull and Bones is the most exclusive organisation on campus. Members have ranged from President William Taft to Henry Luce, the founder of the Time-Life magazine empire, and from Averill Harriman, the businessman and diplomat, to the first President George Bush.

Alexandra Robbins, a Yale graduate and author of a book on the Skull and Bones, Secrets of the Tomb, said: "It is staggering that so many of the candidates are from Yale, and even more so that we are looking at a presidential face-off between two members of the Skull and Bones. It is a tiny club with only 800 living members and 15 new members a year.

"But there has always been a sentiment at Yale to push students into public service, an ethos of the elite making their way through the corridors of power - and the sole purpose of the Bones is power."

The four candidates' time at Yale spans the period from 1960, when Sen Lieberman began his studies, through Sen Kerry's arrival in 1962 and Mr Bush's two years later, to 1971, when Mr Dean graduated - a period that swung through the bright hopes of the Kennedy presidency to tumult and bitterness over Vietnam.

Mr Lieberman and Mr Kerry served on the same committee to oppose resistance to the Vietnam war draft, but otherwise the four appear not to have known each other at the time. They all studied history and political science, however, and had some of the same professors and academic mentors.

Robert Dahl, the then head of the political science department, said: "Many of us had the sense we were preparing future leaders, but I don't think any of us had any idea we were teaching so many presidential candidates."

While at Yale all four showed hints of the varying character traits that would eventually propel them, on different paths, towards the top of American politics.

Mr Lieberman, the grandson of immigrants, arrived from a state school, probably a beneficiary of an unofficial 10 per cent quota of places for Jews that Yale then operated. Politically ambitious, he chaired the Yale Daily News, the most sought-after student position on campus.

Sen Kerry is remembered as "running for president since freshman year". One of his contemporaries said: "He was obsessed by politics to the exclusion of all else. At that age, it's a bit creepy." He dated Janet Auchincloss, the half-sister of Jackie Kennedy, the First Lady, won the presidency of the Yale Political Union, and was initiated into the Skull and Bones before joining the United States Navy for service in Vietnam.

In laid-back contrast, Mr Bush achieved only a "C" grade academically and took little interest in politics. He joined a "sports jock" fraternity and followed his father into the Skull and Bones.

By the time Mr Dean arrived in 1967, Yale was admitting women and setting more store by applicants' academic merit than their social background. The future Vermont governor showed a disdain for Yale politics and resigned from a fraternity order in a dispute over a coffee bar.

Whether the four men's Yale backgrounds is a plus with voters is uncertain. Mr Dean seems embarrassed, once saying he studied "in New Haven, Connecticut" to avoid mentioning Yale by name. Mr Bush makes light of his student years, apparently revelling in his reputation for socialising, not studying.

The Skull and Bones connection is more troublesome. Mr Kerry laughed nervously when questioned about his and Mr Bush's membership on television. "You both were members of the Skull and Bones; what does that tell us?" he was asked. "Yup. Not much," he replied.

Not surprisingly, the club's rituals fascinate many Americans. Robbins's book describes a social club with arcane rules, a hoard of relics ranging from Hitler's silver collection to the skull of the Indian chief Geronimo - plus a resident prostitute.

She says initiation rites include a mud-wrestling bout, receiving a beating and the recitation by a new member of his sexual history - delivered while he lies naked in a coffin. Elevation of a Bonesman creates opportunities for his fellows, and Robbins says that President Bush has appointed 10 members to his administration, including the head of the Securities and Exchange Commission.

She recently surveyed 100 of the estimated 800 living Bonesmen on their preferred election winner - Sen Kerry or President Bush. Perhaps not surprisingly, given that both are pledged to advance the interests of fellow Bonesmen, "They answered that they didn't care. Whichever way it went, it was a win-win for them."