Gordon Brown has finally become Britain's Prime Minister after a long, 13-year wait. It was in 1994 when he and Tony Blair made a deal in which Mr Brown agreed not to stand for the leadership of the Labour Party in return for Mr Blair promising to eventually step down to make way for his would-be rival to take over. Well, three Labour electoral victories later, Mr Brown has achieved his lifelong ambition.

Mr Blair will be a hard act to follow. He was extremely charismatic, an excellent political strategist, a brilliant communicator and he made history for the Labour Party by winning three consecutive general elections. However, Mr Blair always said he would not lead the Labour Party into a fourth general election and the time was therefore right for him to hand over power to his successor. Furthermore, the Conservatives were gaining in strength in the opinion polls and many people in Britain and in the Labour Party thought it was correct for Mr Blair to step down at this point in time, not least because of the situation in Iraq.

Mr Brown's main challenge is to present his government as one of renewal and change, and to persuade voters not to opt for a change in government at the next general election. This will not be an easy task, but it is certainly possible, as John Major discovered in 1992.

Mr Brown's first Cabinet is certainly a massive exercise in change. Every post except Des Browne at Defence (he was also given Scotland) has changed hands, with seven ministers in Cabinet for the first time, in addition to returnees Harriet Harman and Geoff Hoon.

Ten ministers in Blair's Cabinet were either sacked, demoted or resigned. Mr Brown's team includes Britain's first female Home Secretary, Jacqui Smith, Alistair Darling as Chancellor, Jack Straw as Justice Secretary (and Lord Chancellor), and David Miliband as Foreign Secretary - who at 41 becomes the youngest Foreign Secretary since David Owen in 1977.

Mr Brown created three new departments: the Department for Children, Schools and Families; the Department for Business, Enterprise and Regulatory Reform; and the Department for Innovation, Universities and Skills. The Department for Trade and Industry has been abolished, along with the Department for Education and Skills, which has been split into two.

An interesting appointment is that of former United Nations deputy secretary-general Sir Mark Malloch Brown, who has been granted a peerage in order to take up the post of Minister for Africa, Asia and the UN. He will not have Cabinet rank but will attend Cabinet meetings.

Understandably, critics of the new government will call for a change in direction, not just Cabinet members, and that is obviously Mr Brown's greatest challenge. He must seek change and renewal while at the same time be careful not to distance himself too much from the Blair years, during which, after all, he served as Chancellor of the Exchequer.

Here are some of the main challenges I believe Mr Brown faces as he enters a new era at the helm of government, many of which I am sure will be key electoral issues as the next general election:

Iraq is no doubt the number one issue that Mr Brown has to tackle with great urgency. Although Mr Brown was loyal to the government's position under Mr Blair, the war in Iraq - which seems to be getting worse - remains deeply unpopular in Britain. However, Mr Brown certainly has no magic formula here and he will probably stick to the current timetable for the withdrawal of British troops.

In Afghanistan - which is nowhere as disastrous as the situation in Iraq and which many experts say is a winnable war - Mr Brown must convince his Nato allies to send in more troops to stabilise the situation. He must also try to persuade the United States to review some of its tactics in Afghanistan - such as air strikes in built-up areas - which are increasingly turning Afghan public opinion against Nato forces due to civilian casualties.

Mr Brown may want to re-examine the extraordinary close friendship that existed between Mr Blair and US President George W. Bush, which many observers believe was really a one-way friendship and which in reality hardly influenced US foreign policy. We can expect close relations between the two countries to continue, but perhaps on a slightly cooler level.

On the domestic front Mr Brown will probably move away from Mr Blair's presidential style of government, attach greater importance to the House of Commons and rely less on spin - which characterised Mr Blair's time in office to a great extent and with which voters started to feel uncomfortable .Mr Brown is likely to continue with the process of political devolution and Britain could see the introduction of direct elections for mayors in a number of cities (like the direct election for the mayor of London).

Dealing with security and terrorism is another huge challenge facing the new Prime Minister, as Friday's discovery of two huge car bombs in London shows. Mr Brown will have to continue reaching out to Britain's Muslim community to keep them away from Muslim extremism while at the same time being tough on security.

It is likely that Mr Brown will increase the time police can hold terror suspects without charge from the current 28 days. He will also have to push for the resumption of the Middle East peace process and the creation of a Palestinian state, which will lessen the appeal of terrorism to potential Muslim radicals.

Health and education are certainly two priority areas for Mr Brown and are likely to be hot political issues until the election. Despite record spending on the NHS by the Blair governments, many voters are not at all satisfied with the healthcare system and hospital waiting lists are still very long.

It is not clear whether Mr Brown will carry on with Mr Blair's policy of involving the private sector in running the NHS, but clearly a new commitment to improving the health service will have to be made.

Mr Brown will also have to deal with reports of falling school and examination standards as well as pressure from some universities to increase top-up fees above the current maximum of £3,000 a year, something that is likely to be politically very controversial.

Last but certainly not least, Mr Brown has to deal with a eurosceptic public opinion. The new Prime Minister is certainly pro-EU, but is perhaps not as much of a europhile as Mr Blair. Mr Brown now has to steer the new European Union Reform Treaty - which Tony Blair agreed to - through Parliament, and will have to convince the public that the treaty is not a European Constitution "through the back door" as the Conservatives will no doubt claim.

Mr Brown has a number of challenges ahead of him and he will have to do what French President Nicholas Sarkozy managed to do - convince voters that despite being in government over the past years he is the man of change and not the opposition. It won't be easy, but it is certainly possible.

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