In his keynote speech, he is expected to put pressure on Prime Minister Tony Blair and Sinn Fein on the thorny issue of the decommissioning of paramilitary weapons.

In spite of Mr Trimble's recent success in securing the Nobel peace prize for his part in the Northern Ireland peace process, there is unease among the unionist ranks over some of the consequences of the Good Friday Agreement - in particular the absolute refusal of paramilitary groups to decommission their weapons, and the early release of paramilitary prisoners.

The main bone of contention for unionists lies in the imminent setting-up of cross-border bodies for co-operation with the Irish Republic.

Mr Trimble (left) with fellow Nobel prize winner John Hume

For these bodies to be established, many say, the executive, or cabinet, of the new devolved assembly has to be put in place.

Sinn Fein is entitled to two seats on this executive because of its electoral support. But some unionists believe that the republicans should not be allowed on to the executive while the IRA hold on to their weapons.

These unionists are likely to put pressure on Mr Trimble to stick to his word and bar Sinn Fein from taking its seats on the executive until the IRA starts decommissioning its arsenal.

At a meeting on decommissioning with Mr Blair on Monday, Mr Trimble restated his previous warning that republicans must start handing over weapons before Sinn Fein can take up seats in the Assembly.

Decommissioning as soon as possible

It is thought that Mr Trimble will indicate in his speech that Mr Blair should not back down on his promise to ensure that decommissioning should begin as soon as possible.

And to republicans he is likely to signal that they will not have their places in the new executive of the devolved assembly until the IRA begins to hand over its weapons, although there is still time for them to do so.

A further challenge to Mr Trimble could come in the form of the pressure group Union First which has recently been founded within the ranks of the Ulster Unionist party. Some Trimble loyalists view this group as the basis for a possible leadership challenge.

External pressures

Mr Trimble - also First Minister of the new Northern Ireland Assembly - faces continuing pressure from outside his own party.

Leaders of Sinn Fein, are blaming him for the current gridlock in forming a cross-community government.

Meanwhile the SDLP of John Hume, with whom Mr Trimble shared his Nobel prize, says the unionist leader is wrong to insist on disarmament now, since the Good Friday agreement specifies only that it should happen by mid-2000.

The BBC's Ireland Correspondent Denis Murray says that Mr Trimble's standing within his own party remains strong and the Londonderry conference is unlikely to be a turbulent affair.

But the leader of the Ulster Unionists will need to tread a careful path between the left and right wings of his party - for one, to avoid sacrificing the future of the Good Friday agreement by rigid adherence to principle and for the other, not to succumb to pressure to make peace at any price.