Brightly coloured sight-seeing buses cruise along the Falls Road, with rain-soaked heads turning as the guides point out the headquarters of Sinn Fein: this is post-Troubles Belfast.

But inside the building, things are not at all relaxed: it is a hive of activity, with men and women bounding purposefully up and down the stairs and in and out of the building. “That door never stops,” said the cheerful republican on security duty.

There used to be a great deal of overlap between Sinn Fein and the IRA, but now the ‘armed struggle’ is no more. Once a centre of subversion, the office is now strictly confined to the business of politics.

This is one of the offices used by Martin McGuinness, once regarded by Downing Street as a republican with “first-hand operational experience”. Now, as Deputy First Minister, he also has another office in Stormont Castle, once occupied by the British ministers who used to run Northern Ireland.

Today Westminster shares power with Belfast's devolved government, which last year came into being amid widespread amazement and a general welcome for what was seen as an epic breakthrough.

McGuinness, a one-time icon of militancy but now a symbol of his movement's politicisation, readily acknowledged the difficulties within the administration that was headed jointly by Sinn Fein and the Democratic Unionist Party. Not too many years ago, talk of difficulties often brought warnings of a possible surge in violence. Today, this element is gone. There will certainly be crises ahead, but they will be political, and not matters of life and death.

Time was when many viewed McGuinness as one of those who kept the Troubles going, blaming him for prolonging the conflict. Many felt exactly the same about his loyalist counterpart, the Rev Ian Paisley. Yet the general perception of both men changed dramatically last year, when Sinn Fein and the DUP formed their governing coalition. Most people were, in the words of McGuinness, “gobsmacked and amazed” that they could make peace after all those decades of implacable enmity.

A double act developed, characterised by so much bonhomie and good cheer that McGuinness and Paisley became known as the ‘Chuckle Brothers’. Paisley (like the IRA) has now left the scene, to be replaced as First Minister by his deputy, Peter Robinson. Of Paisley, the republican leader says: “I respected his mandate, I respected his age and the courageous decision that he took to come into government.”

He recalled how attitudes towards them changed overnight. “Ian Paisley and I would tell each other stories about the people who approached us after making the deal,” he said. “He told me about coming off a plane at Heathrow, and this woman came over and said, ‘Mr Paisley, can I shake your hand?' And he said yes, and they shook hands. Then she said that a couple of months earlier she wouldn't have shaken his hand; she would probably have slapped him on the face — and it turned out she was the Mother Superior of a nunnery. But she praised him to high heaven and said he had done a good thing and wanted to say thanks."

McGuinness has had similar encounters. “I told him about being in the City Hotel in Derry, and this woman came running up to me and said, ‘Can I give you a big hug?' And I said yes, and she hugged me. Then she said, ‘I wouldn't have given you a big hug before this — I'm an Ian Paisley supporter, but I think what you've done is absolutely tremendous.' That happens to me all the time. I think that tells you how things have changed, and that something very, very powerful has happened. And it's not just on this island.

“In all the times I've travelled to London since 1994, everybody that comes up to me tells me to keep up the good work. I haven't heard one angry voice, which is absolutely amazing.” But does he get such reactions from people who have specifically suffered at the hands of the IRA? “I meet people all the time who have been hurt by the IRA,” he replied. “Some of the most humbling moments are meeting those people, and they put out their hands and say, ‘Well done, this is good, keep it going.'”

He once received a letter asking for a meeting from a number of disabled police officers. It produced, he said, “all sorts of opinions within Sinn Fein” on whether to hold such a meeting. “But I met them,” he recalled. “When they came into the room. it was clear they were disabled as a result of the conflict and as a result of being injured by the IRA. But they shook hands and said, ‘We're here to say we support what you're doing, that we support this process.'”

The IRA killed many police officers, but now Sinn Fein supports policing and justice: McGuinness has paid hospital visits to a number of officers who have been injured in attacks by dissident republicans.

Of violent dissidents, he commented: “Those people think that more car-bombing, more military activity, is going to bring about the freedom of Ireland, but they're living in cloud cuckoo land. They need to recognise and understand that we're in a new situation, and that there cannot be — under any circumstances whatever — any contemplation of going back to the bad old days. People should assist in the apprehension of those who are involved in these deeds.”

To splinter groups, he said: “My message is that it is a totally futile exercise that runs totally contrary to what the people of Ireland as a whole want. Any attempt to plunge us back into the violent days is not going to be supported. Do they really want to see 20,000 or 30,000 soldiers back on the streets?”

The Deputy First Minister gets up at 5.30am each day to drive from his home city of Londonderry to Belfast. Then it's attending the Northern Ireland Assembly, chairing and taking part in meetings, signing letters, studying documents, seeing delegations until eight or nine o'clock in the evening.

McGuinness has never met David Cameron, though he has met members of the Shadow Cabinet. Gordon Brown, he said, has been through “excruciatingly difficult” times.

In common with other political figures, he reported that there is “huge interest, absolutely amazing interest” in the Irish peace process from further afield, citing visitors from Sri Lanka, the Middle East, the Basque country and elsewhere.

He has travelled to Helsinki and Baghdad for talks on Iraq. “All we can do is offer our experiences. I tell them that without decisive leadership, it is almost impossible to resolve conflict. We have no delusions of grandeur about our abilities to resolve those conflicts — but if it saves lives, why not negotiate now?” Could that not apply to Ireland as well? “We have to recognise that, in the final analysis, we got it done,” he responded. The performances of McGuinness and his party's president, Gerry Adams, were both commended in the recent book on the peace process by Tony Blair's chief of staff, Jonathan Powell, who spent many hours engrossed in often tense negotiations with them.

Powell wrote: “It was a remarkable act of leadership by Adams and McGuinness to talk the IRA into peace and to persuade them to settle for something far less than they had demanded in 1993.”

The peace process is now at yet another tricky point, since Paisley's replacement in June by the markedly less jovial Peter Robinson. Sinn Fein figures complain that few major governmental decisions have been going their way.

McGuinness is reserved, but not hostile, when talking about his new governmental partner. “I have entered into the relationship with Peter Robinson with a commitment and dedication to make it work,” he said.

“I think it's fair to say there have been difficulties, but my assessment is: why would he not want it to work? It's still early days in the leadership of Peter Robinson, but I'm working on the basis that he wants this to succeed. I'm optimistic.”

There are grumbles, in the republican grassroots, that the DUP is blocking what Sinn Fein would like to see happening in important areas such as policing and justice, education reform, the status of the Irish language and the future of the old Maze prison.

McGuinness acknowledged that there was a certain amount of restlessness and frustration in the republican community, and added: “I suppose that has been a feature of the process from the very beginning — people are impatient for change, and I think rightly so. Nobody could say with their hand on their heart that, at this stage, the institutions have delivered everything that people want. But I think what they want to know is: are they beginning to deliver and is the potential there for delivery?”

The power-sharing executive clearly has its stresses and strains: republicans, as ever, want rapid movement on various fronts, while loyalists, as usual, are suspicious of wholesale change. Robinson is certainly in favour of the settlement, but some in his party want to see rather less chuckling and rather more opposition to the republican agenda.

McGuinness is hopeful. “A Rubicon has been crossed by everybody, and the project for me now is to ensure that there can be no going back. This is the only sane and sensible way forward for all of us,” he insisted. “This is the best way to break down the old hatreds and divisions.”

What has he learnt in the course of his controversial, incident-packed career? “Compromises have had to be made: compromise is a dirty word in the course of Irish politics, but people recognise that they had to be made,” he said.

“I'll tell you what I've learnt. I've learnt that nothing is impossible — that no matter how things are, if there's a will to find a way through, then a way will be found.”