George W. Bush's meeting last week with Russian President Vladimir Putin and his forthcoming meeting with Chinese leader Hu Jin Tao are a reminder that Bush and his successors will continue to face the challenge of dealing with these two unfriendly and potentially dangerous powers. Much of the world has moved toward democracy and freedom, but China hasn't much and Russia seems headed in the opposite direction.

Of the two, China is probably easier to deal with. It appears to have a collective leadership, which gives a certain continuity to its policy.

The bad news is that the regime continues to suppress freedoms of speech and religion. Those within it who dissent seem to be jettisoned, as Zhou Ziyang was when he argued against the violent suppression of the Tiananmen Square protesters in 1989.

The good news is that the collective leadership seems to be producing rational decisions responsive to events. The Chinese leaders have evidently moved the rogue North Korean regime in the direction of curbing its nuclear weapons programs. Apparently, they recognize that Kim Jong Il is a danger to China as well as to us.

Russia is different. Putin seems to be persisting in his irrational opposition to our decision to put missile defense installations in Poland and the Czech Republic. As Bush has pointed out, it's obvious that these are no threat to Russia -- they're clearly designed to protect Europe against an Iranian missile attack. Putin's apparent desire to assert some kind of hegemony over what were once the Soviet Union's Eastern European satellites seems delusional.

But one man's delusions can move national policy in a country where the former KGB officer seems to have consolidated power in his own person. He appears in complete control of the government, which in turn controls the oil industry and the news media. And while he has reiterated that he will respect the law, which prevents him from running for re-election in 2008, he seems to be single-handedly picking his successor.

The Russian political system has come to resemble the political system of Mexico from 1929 to 2000, which was something of an absolute monarchy, with term limits. The candidate of the ruling PRI was always elected president, the legislature was a rubber stamp, and the incumbent president chose his successor. How this worked in practice is the subject of "Perpetuating Power: How Mexican Presidents Were Chosen," a fascinating book by former Mexican Foreign Minister Jorge Castaneda. He interviewed four Mexican presidents, who discussed frankly how they had been selected by their predecessors and how they, in turn, chose their successors. Only someone as well connected as Castaneda, who grew up as part of the PRI elite (his father was also foreign minister) could have elicited the almost Shakespearean accounts.

The continuing theme was that the outgoing president sought to exert power in the reign of his handpicked successor -- and failed. The pattern was set early on. The originator of the PRI system, Plutarco Calles, tried to run things after his choice as successor, Lazaro Cardenas, took office. Cardenas called Calles into his office and told him that he had to stop and he could no longer live in Mexico. Calles moved to California, although he was eventually allowed to return to Mexico.

My guess is that Putin, as he decides whom to choose as the new president, hopes to continue to exert power himself. And that he will probably find himself shut out, as Calles was. Or as Boris Yeltsin, who single-handedly chose Putin to succeed himself in 1999, was.

The problem for the United States is that this kind of regime will tend to behave less predictably than the collective regime of China. In Putinist Russia, as in PRI Mexico, each new leader may lurch from policy to policy. Many such changes will not be predictable, because politicians contending to be selected by one man for a position of paramount power will not show him anything they think he doesn't want to see. As Castaneda's book shows, one-man rule tends to produce a sycophantic court and new leaders who do things no one expected.

Thus, Putin has veered off Yeltsin's course, suppressing the free press, menacing independent leaders in former Soviet republics and opposing efforts to keep Iran from developing nuclear weapons. We can only hope that the next Russian president veers off Putin's course, as well.