On Wednesday or Thursday, Londonderry's MP and most famous citizen, SDLP leader John Hume, is to deliver to the Irish government a report which, some optimists dare to hope, could signal the beginning of the end of the troubles.
Mr Hume was among those at the march which was broken up by RUC batons on 5 October, 1968. This episode focused British and international attention on a problem that has since claimed more than 3,000 lives.
The faint new hopes for peace are based on one thing only: his judgement that, after a bloody quarter of a century, the conditions may now be right. But in addition, Mr Hume's high-risk exercise in talking to Gerry Adams of Sinn Fein must be predicated on the belief that republican leaders are genuinely interested in talks.
It follows that he must also believe that Sinn Fein and the IRA are prepared to consider a negotiated settlement, and have moved from the traditional republican vision of one day simply accepting a British surrender on their terms.
If this much is correct, then the chances of making a real advance are closer than most observers had thought. But there would still be many obstacles ahead. The next step is for Mr Hume to make a report to the Irish government. This is expected to take the form of a meeting with the Taoiseach, Albert Reynolds, and Irish Foreign Minister, Dick Spring, in Dublin on either Wednesday or Thursday. Irish ministers do not have a precise idea of what Mr Hume will say to them. His reputation is such, however, that no one in Dublin believes he is involved in a cosmetic exercise or anything from which the republicans could draw propaganda advantage.
At the same time, it is not believed Mr Hume is about to come up with some magical plan for peace. One source said: 'I'd say that John has spotted an opening or an idea that might be developed. He presumably senses that he's got enough positive vibes from Adams that it's worth trying to build on it.'
If the Irish government is convinced that the Hume-Adams venture could produce something of substance, its own position becomes extremely delicate. Dublin, no less than London, holds fast to the stance that there can be no negotiation with Sinn Fein while the terrorist violence lasts.
The question would therefore arise of how matters could be advanced while Sinn Fein is kept at arm's length. The next step would be for Dublin to convey to the British government the reasons why it, and Mr Hume, believe the process of talking to the republicans should be continued.
The British government would have to reach its own judgement on whether, and how, to encourage talks. By this stage two other major factors would be in play. The first is whether republican diehards would emerge to oppose Mr Adams's approach, questioning whether he had become involved in a 'sell-out'. This is a real possibility: Mr Adams has already strayed into areas unfamiliar to standard republican rhetoric in his joint statements with Mr Hume.
The second factor is a potential loyalist backlash. Already this week, Unionist politicians have closed ranks, with both moderate and extreme elements denouncing Mr Hume in the most ferocious terms. The fear is that their paramilitary counterparts will attempt by violence to knock this most delicate set of manoeuvres off course.