By Jan Repa
BBC Europe analyst
Last week, Romania concluded membership negotiations with the European Union. A number of EU officials and MEPs have openly expressed their misgivings.
Basescu's supporters have many expectations, but will he deliver?
Not only is Romania considerably poorer than the ex-communist countries of Central Europe - the Czech Republic, Hungary, Poland and Slovakia, which joined the EU in May. It also has the unenviable reputation of being one of Europe's most corrupt countries.
Romania's corruption has been described as "endemic": not so much a problem to be overcome, as an integral element of the way Romanians conduct their business and politics.
Prime Minister Adrian Nastase's Social Democrats and Mr Basescu's two-party Truth and Justice alliance say they want Romania to become a successful and respected member of the EU club. But can Mr Basescu deliver?
While Prime Minister Nastase won most support in Romania's smaller towns and countryside, Mr Basescu did well in the cities, notably Bucharest.
Relying on middle class
Like ex-communist parties elsewhere in Central and Eastern Europe, Mr Nastase's Social Democrats rely on a dense network of local patronage and influence, often going back to the days of Communist rule. No party in Romania is free of corruption.
But, according to observers, Mr Basescu's Truth and Justice alliance relies rather less on this kind of influence.
Mr Basescu's electoral success is also said to reflect the emergence of a younger, educated "middle class", embarrassed by Romania's culture of graft and patronage, and keen to see the country embrace "Western" norms.
Mr Basescu has promised tax cuts and has described corruption as a "threat to national security".
He has also defended homosexuals - a risky step in a country where public attitudes to sex remain, by the standards of most European countries, deeply conservative.
More controversially from the EU's point of view, he says he wants to renegotiate the parts of the EU accession agreement dealing with energy and steel.
Opponents in parliament
He has also signalled a desire to work more closely with America - stressing Romania's geographical location on the Black Sea, on the borders of the former Soviet Union, and talking of a "strategic partnership" with Washington and London.
Mr Basescu now needs to nominate a new prime minister.
Last month's Romanian parliamentary elections gave Mr Nastase's Social Democrats the largest number of seats - but not enough to form a government on their own.
The Social Democrats say they want to remain in government - and will almost certainly try to continue their previous alliance with MPs representing Romania's Hungarian minority.
If Mr Basescu insists on nominating a new prime minister from his own Truth and Justice alliance, or if the Social Democrats cannot muster a majority, there could be deadlock.
New parliamentary elections could be the only answer.