First Belarus, then Ukraine. Elections in the two former Soviet republics that are the closest eastern neighbours of the European Union have produced uncomfortable results for those who believe in peaceful democratic revolutions.

In Belarus, the liberal opposition failed to make any inroad on the ruthless machine of Alexander Lukashenko, the country`s irascible and autocratic ruler. His massive security machine - employing an estimated one in 10 of the population - ensured that the entire electoral process was heavily skewed in his favour. Even if it had not, most observers reckon that the maverick dictator would have won.

On Sunday, Ukraine offered a far more democratic alternative in its parliamentary elections. They produced a predictable defeat for Our Ukraine, the party supporting President Viktor Yushchenko and his platform of liberal economic reform and ever-closer relations with the EU. His party came a poor third, paying the price for his failure to deliver much progress with those reforms, or bring the country appreciably closer to the EU.

The results in both Belarus and Ukraine demonstrate that the influence of the European Union on its "near abroad" is distinctly limited. It can easily be exaggerated - not least by suspicious Russians fearing interference in their own backyard.

Take the Ukraine election. On one level, the result is rather good for democracy in that country. Top of the poll was Viktor Yanukovich, the candidate backed last time by the Russian government, and second was Yulia Tymoshenko, the populist prime minister whom Mr Yushchenko sacked last year. There was no attempt to fix the result in Our Ukraine`s favour.

On the other hand, the slump in Mr Yushchenko`s popularity raises the question whether the EU could or should have done more to help him. Ever since he came to power in January 2005, he has been unable to show many tangible gains from his pro-EU attitude.

The answer is that the EU probably should have done more, but the politics of the 25 member states make it almost impossible to do so.

For ordinary Ukrainians, the most relevant part of the relationship with the EU is visa policy: the ability to travel more freely is a liberation in contrast to the old days of Soviet rule. It is also an opportunity for travellers and above all students to see what the rest of Europe is like, including its institutions, its market economy, and its rule of law.

Progress in negotiating a more liberal visa regime has been painfully slow. There is a danger that instead of getting cheaper and easier, visas will be more expensive: EU ministers are debating raising the price from Euro35 to Euro60.

Perhaps more ominously for the 2m-odd Ukrainians who cross the border on visa-free shopping trips to Poland every year, that country wants to become a full member of the Schengen zone from October next year: from then, full Schengen visas will be required of Ukrainians.

Yet liberalising visas looks very different from a west European perspective. Ukraine is seen as a notorious source of cross-border people trafficking into the EU. When Germany relaxed its visa regime in the late 1990s, the government was accused of causing an upsurge in prostitution, although many probably came with false documents, not valid visas.

Ukraine will only be allowed an easier visa regime if it signs a readmission agreement to accept back any illegal immigrants coming from or through its territory. That is taking months to negotiate.

In the meantime Russia has succeeded in signing a much more favourable arrangement.

The problem is even more difficult for Belarus, thanks to the frozen state of relations between the government and Brussels. There is little chance of an easier visa regime in the near future for the benighted Belarusans. At least Ukraine is moving slowly in the right direction.

Poor Belarus looks likely to be lumbered with Mr Lukashenko for the foreseeable future.                         

The article was monitored by The Action Ukraine Report (AUR) Monitoring Service, Morgan Williams, Editor.