Press digest from the two countries:
Here's a unique sample:
MAX BOOT IN THE NEO-CONSERVATIVE MAGAZINE COMMENTARY
It's not the weapons, it's the regimes that matter. Personally, I don't feel much safer knowing that Russia will have a few hundred fewer strategic warheads, especially when they still have thousands of highly portable tactical nuclear weapons that aren't covered by this treaty at all. Russia will continue to be a destabilising and dangerous influence as long as it has an unaccountable government with few, if any, internal checks and balances. That is the real source of American-Russian tension, and by further legitimating the existing Russian regime we are, if anything, slightly exacerbating that problem.
ANALYSIS Jonathan Marcus, Moscow
President Barack Obama's speech began with conventional references to Russia's timeless heritage. He mentioned the Russian people's suffering during World War II.
There was inevitably some geo-politics. Mr Obama said that "the days when empires could treat sovereign states as pieces on a chess board are over". That will be taken as a clear stab at those in the Russian leadership who still see their former-Soviet neighbours as a Russian sphere of influence.
But in his choice of audience - students from a business school "founded with Western support but now distinctly Russian" as he put it - he was hinting at the sort of society he hoped Russia would become.
*A nice rhetorical move by Mr.Obama here. Mind you, he's not lying if he genuinely believes that the USSA is not an empire.
Mr Obama urged the fellow nuclear power to respect international borders, human rights and democratic principles, as well as tackle corruption.
"People everywhere should have the right to do business or get an education without paying a bribe," he said.
"That is not an American idea or a Russian idea - that's how people and countries will succeed in the 21st Century."
Mr Obama then went on to hold what the White House described as a "good meeting" with former Soviet President Mikhail Gorbachev.
On Monday, after meeting Russian President Dmitry Medvedev, Mr Obama signed eight separate agreements with Russia.
These, he said during the speech would "substantially reduce our warheads and delivery systems".
Among the deals was a pact to negotiate a new arms control treaty to replace the 1991 Start I pact which expires in December.
A new agreement could see the two countries reducing their nuclear warheads by up to a third, to below 1,700 each within seven years of the treaty's signing.
Obama urges shift in Russia ties