Members of the delegation have already made about a dozen trips to Northern Ireland over the past two years, most recently during Sinn Fein's elongated internal debate on the Downing Street Declaration, which ended in its rejection by hardcore elements.
Sinn Fein and the IRA have long been obsessed with winning the support of the Irish-American community, something that has largely been denied them because of the IRA's campaign of terror. While staunchly opposed to violence, many influential Irish-Americans remain sympathetic to republican aims and have earned the trust of Sinn Fein leaders, most notably Mr Adams.
Since President Bill Clinton's election, they have been telling Mr Adams - and through him the IRA - that an opportunity exists to further their political agenda without violence. They point out that there is a Democratic president whose relations with the British government are distinctly cool.
A member of the delegation, Niall O'Dowd, publisher of the Irish Voice newspaper in New York, said: 'We believe the time has never been more opportune for a peace initiative. There is an understanding between Hume and Adams, sympathetic governments in Dublin and London, a reasonable leader of the Ulster Unionist Party in James Molyneaux and an American president who has taken a personal interest in the issue. There is also a new level of sophistication in Irish America which can help smooth the peace process and events afterwards.'
Members of the delegation have access to the highest levels of the Clinton administration and have received enthusiastic backing for their work from the Irish embassy in Washington. They won a first victory earlier this year when they persuaded the Americans to provide Mr Adams with a visa to visit New York over the ferocious objections of the British government.
Their return to Belfast comes amid speculation that an IRA ceasefire is about to be declared. One of the delegation's main roles will be to offer a psychological boost to Sinn Fein as it prepares to make the ceasefire decision.
Another member of the group, Bruce Morrison, a former congressman, said: 'We've continued to try to help Sinn Fein to persuade the IRA that the time has come to move from violent acts to the political arena and end the armed struggle.' One of his concerns now is that 'somebody has got to stop the loyalist killings' and he expects numerous private calls on John Major encouraging him to crack down on loyalist paramilitaries.
Mr Morrison, who is about to join the Clinton administration as Federal Housing Finance chairman, believes that the President's cool relations with Mr Major 'are not unrelated to the situation in Ireland' and says that with peace 'Britain's only problem in the US would go away'.
The other members of the delegation are wealthy businessmen, William Flynn, of Mutual of America, and Charles Feeney, head of the multinational General Atlantic.
If there is a ceasefire, it is expected that the US will grant Mr Adams a multiple entry visa, which will enable him to tour the US raising support for the republican movement in advance of talks on a constitutional settlement on Northern Ireland, in which he expects to play an important role.
And end to terrorist violence by the IRA is also expected to lead to a dramatic increase in US investment in Northern Ireland. The Irish- American lobby has already mooted the possibility of launching 'Ireland Peace Bonds' to be underwritten by London and Dublin. Income from such bonds would be distributed without the present discrimination against projects run by Sinn Fein.
Diplomats stress that there are no formal links between the Irish-American delegation and either Mr Clinton or the Dublin government. 'They are not negotiating on behalf of the White House; there is no new package and Gerry Adams knows exactly what he has to do,' a diplomatic source with knowledge of the delegation's activities said. 'None the less they could prove crucial in persuading the IRA that it is time to change.'
During a visit to Northern Ireland last September, negiotiations with Sinn Fein led to a seven-day cessation of violence by the IRA. This was taken as a signal by the White House that a serious peace effort was afoot and led ultimately to Mr Adams getting a visa to visit New York.
Mr O'Dowd said that the delegation is trying to build on the Downing Street Declaration and the work of the Irish and British prime ministers.
The Hume-Adams dialogue, along with the secret talks with the British government and the subsequent Downing Street Declaration, had a profound impact on the Irish-American community, which for years has been bitterly divided between supporters and opponents of the IRA.
The dialogue between Mr Hume and Mr Adams healed wounds in the Irish-American community, bringing influential politicians like Senator Teddy Kennedy, who have always opposed the IRA, into the same camp as republican sympathisers.
Mr Adams and many in the republican movement closely follow developments in the US, believing that once united, the Irish-American lobby could be influential in persuading Washington to lean on London.
Mr Adams has also been promised that President Clinton could play an active role if an escalation in loyalist killings threatens a ceasefire.
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