Conflict of interests
The conflict of interests involves Nato's historic open-door policy on the one hand, and on the other hand Russia's feeling that the alliances' borders are growing too close for comfort.
Nato was set up in 1949. It was an alliance to counter the military power of the Soviet Union.
The Soviets in turn set up the Warsaw Pact and a clear Cold War line was drawn between the two sides.
The Warsaw Pact was dissolved in 1991 with the collapse of the Soviet Union and Nato's eastward expansion began.
Shadow of Russia
At the Bucharest summit, Albania and Croatia too will begin the formal process of their membership.
Nato's backing of a US missile defence system in Poland and the Czech Republic has been harshly condemned by Vladimir Putin.
The Russian president will be making his first appearance at this year's summit to express his fears of a new arms race.
Jaap de Hoop Scheffer, Nato's secretary-general, says: "If President Putin comes to Bucharest with an open mind, it should be possible for us to advance a broader Nato-Russia relationship."
Nato says its eastward expansion will not threaten Russia.
Still, Jonah Hull, Al Jazeera's correspondent in Kiev, says Ukraine and Georgia are unlikely to be given this membership action plan in Bucharest.
"The problem they face even with President Bush's support is opposition both from Russia and from significant members of the Nato alliance.
"Russia has long been wary of Nato's expansion eastwards. It views it as a provocation and even says it will aim missiles at Ukraine if it goes ahead."
Russia's differences with Nato go beyond the proposed eastward expansion.
Moscow is also upset by Kfor - a Nato-led peacekeeping force that remains in recently declared independent Kosovo.
All of this has threatened to shift the focus of the Bucharest summit away from Afghanistan, supposed to be at the top of the agenda.
Nato leads more than 47,000 military personnel in that country.
Bush wants member countries to send more troops to Afghanistan.
"The alliance must maintain its resolve and finish the fight ... we cannot afford to lose Afghanistan," Bush said in Bucharest during a speech at a German Marshall Fund conference on Wednesday.
He said that if the alliance does not stay on the offensive in Afghanistan, Taliban and al-Qaeda fighters will use it to launch more attacks on the West like those on September 11, 2001.
Only a few countries have so far answered the call for more support to fight the Taliban in the south.
Last week, France committed more troops to Afghanistan.
Nicolas Sarkozy, the French president, confirmed on Thursday in Bucharest that France will send a battalion and special forces to Afghanistan to join the Nato mission there.
The additional soldiers partially meets demands by Canada, which had threatened to withdraw forces if Nato allies did not send reinforcements.
Up to 81 Canadians have been killed in Afghanistan since 2002.