POLAND HAS NOW launched itself into the great leap from centralized Communist rule to a market economy -- a transition requiring great political courage. While the same leap lies ahead of all of eastern Europe, the Poles have gone farther and faster than the others. It has often been said that there is no precedent in modern experience for this enormous transformation, and in the strictest sense that's true. But it's not entirely a leap in the dark. Half a world away, the Poles can see an interesting model -- and a highly promising one -- in Mexico.

The differences between the two countries' situations are too obvious to require much elaboration. The similarities, less conspicuous, deserve notice. While Mexico was never a police state, its long tradition of authoritarian one-party politics is only now dissolving. Both Mexico and Poland entered the 1980s with their economies largely closed to the outside world. State ownership never went as far in Mexico as in Poland, but a decade ago nearly half of Mexico's GNP was in the public sector.

The standard of living is a little higher in Poland, but in both the GNP per person is just under $2,000 a year. That puts them, in a worldwide comparison, in roughly the middle -- 10 times as rich as the really poor, and one-tenth as rich as the really rich.

Mexico, pitched into crisis by its foreign debts and the falling oil prices of the early 1980s, now has had seven or eight years of experience with reform on an almost revolutionary scale. The first thing that the Mexicans had to do was to get inflation under control and eliminate the budget deficits that were generating it. During the past year the Poles have made great progress in that same struggle. The Mexicans opened up their country to foreign trade and competition, as the Poles also have done. The Mexicans have been able to negotiate sharp reductions in the burden of debt service, an exercise that still lies ahead of the Poles. The Mexicans have sold hundreds of formerly state-owned enterprises to private owners. They are now the world's leaders in the art and science of privatization, a process just getting under way in Poland.

None of this has been painless. Mexicans suffered a dire drop in living standards in the mid-1980s and have only recently begun to recover. Some Poles may wonder whether reform is worth it. But the Mexican economy is growing again, and quite rapidly. Capital is moving into the country from abroad, and investment is rising. Transforming a country's economy takes not only courage but great patience and stamina as well. Prospects for Mexicans are better than they have been for decades -- and, although Poland is at a much earlier stage of the process, that's true for the Poles as well.