World leaders have for years struggled to determine which ones to recognize, often making decisions and then trying to limit the repercussions by warning that each situation is unique.

The questions now are: whether that hesitance to bestow recognition could be eroding, as witnessed by Kosovo and Russia’s action in Georgia; and whether other independence movements will use the recognition of the two enclaves to further their own ambitions by citing similar grievances. Not far from Georgia, for example, is an Armenian enclave that wants to secede from Azerbaijan, and Kurdish separatists are seeking their own homeland in regions of Turkey and Iraq.

In the past, most countries feared that if they waded into one such conflict, it could be used against them in a future one. On Tuesday, no other big power followed Moscow’s lead and voiced support for South Ossetia’s and Abkhazia’s independence.

Many in Abkhazia have expressed the desire to be separate both from Georgia and Russia  and some experts say it might be viable as an independent nation, albeit a very small one, because of its larger size and busy port.

South Ossetia, in contrast, has only 70,000 people and borders on the Russian region of North Ossetia. Suspicions have long arisen that after seceding from Georgia, South Ossetia would be absorbed by Russia and joined with North Ossetia  and most Ossetians say they support that.

The Kremlin said Tuesday that it had no plans to take over South Ossetia. It has already given Russian passports to many residents of both places, thereby widening its influence.

Image Residents of Tskhinvali, South Ossetia, rejoiced Tuesday after Russia recognized South Ossetias and Abkhazias independence. Credit... Sergei Karpukhin/Reuters

Mr. Medvedev announced the enclaves’ independence with unexpected swiftness, only a day after the Russian Parliament unanimously called upon him to do so. Diplomats and analysts had surmised that the Kremlin might draw the process out as part of negotiations with the West.