DRUGS remain a gnawing problem on the streets of the United States. But over the border, in Mexico, the drug problem takes on a different dimension. There, the problem isn't consumption, but drug-related corruption on a scale that threatens to engulf the country - even as it struggles to stop an economic downdraft and realize some of the promise of the North American Free Trade Agreement. When heightened US interdiction closed down air and sea routes into southern Florida in the late 1980s, the cocaine trade shifted to the land route through Mexico. Traffickers in Mexico's coastal and northern states became drug barons, with cartel structures rivaling those of their Colombian suppliers. Mexico's government, under President Ernesto Zedillo, has vowed to go after the traffickers - and it has, in fact, jailed some notorious figures. But the drug lords have gone after the government too - and in numerous instances they've gotten their man. Reports out of Mexico indicate that officials ranging from local policemen to federal attorneys general have been paid off. Police trying to arrest traffickers have sometimes fought those paid to protect them. The illegal drug business generates $7 billion a year in Mexico, according to US Drug Enforcement Agency estimates. That's a lot of cash to spread around in a country where incomes have plummeted and where government by payoff existed long before the cocaine commerce. Mr. Zedillo has termed the drug trade the greatest threat to Mexico's security. His efforts to stem that trade are apparent. But drug trafficking is only one of many difficulties facing Zedillo as he completes his first year in office. It is, however, a problem with distinct implications for the Mexico-US relationship. The economic partnership so touted during NAFTA's incubation will have trouble taking hold if cocaine is perceived as a chief Mexican export. The drug issue has often proved a potent weapon for US politicians inclined to attack stronger economic relations with Mexico. Mexico's campaign against traffickers and the corruption they breed has to be seen as vigorous. Other countries, such as Italy, have anticorruption experience that could spawn ideas for strengthening Mexico's judiciary and police. But even intensive cooperation between US and Latin American authorities has so far been inadequate to stop the flow of drugs to US consumers. The US can probably be of most help to Mexico by persisting in its own efforts to quell the demand for drugs shipped northward. The economic partnership won't take hold if cocaine is seen as a chief Mexican export.