HUNTING DOWN THE DRUG RUNNERS

At 01:29 hours on Dec. 13, the Diligence takes up ''covert surveillance'' of what amounts to no more than a blip on a radar screen. That blip is the American Hope, a 73-foot fishing boat from Aransas Pass, Texas, cruising in international waters between Cuba and Mexico.

The fishing vessel's course fits the classic profile of drug runners from Colombia to the United States. They avoid Mexican authorities by moving just outside that nation's claimed territory, and just within the 15-mile zone the Coast Guard maintains. Their speed may be slightly faster than numerous commercial fishing boats, and eventually they must head northeast to cross the Gulf of Mexico.

Just over the horizon, and out of the smaller craft's radar range, the Diligence follows and waits for a chance to slip between the ''druggie'' and the safe zone.

Only after daybreak does the runner make the telltale course change. After the vessel reaches more than six miles beyond the buffer, the 210-foot cutter gives chase, pulling alongside at 11:46. At 11:49, with its captain, Comdr. J.G. Schmidtman, in direct command on the bridge, the Diligence orders the American Hope to ''heave to.''

Outrun and helpless at close range, the vessel offers no resistance. In the cutter's launch, a heavily armed Coast Guard boarding party circles the fishing boat once, orders the crewmen to the stern, and demands that they put their hands on the railing.

One of the fishing boat's crew points to the aft hold and says, ''What you are looking for is in there.''

But the Coast Guardsmen ignore him. They must follow a strict procedure, and they play the script to the letter. No search, as such, may be carried out. They are legally on board to conduct an administrative inspection of safety gear and documentation. They can also make a ''security sweep'' to guard against being surprised by anyone who may have concealed his presence.

Thus, 12 minutes elapse before word is radioed back that a ''green leafy substance'' is being tested for ''THC,'' the active ingredient in marijuana. The holds are piled high with 20 tons of the drug, with a street value of at least $ 12 million. Its odor is noticeable even on deck. At 12:25 the crewmen are arrested, read their rights, and searched.

More marijuana was seized by federal agents in the first nine months of 1982 than in all of 1981. Seizures of other drugs, including cocaine and heroin, was greater in 1982 than in 1981.

But no more than 10 percent of the drugs smuggled into the US is seized by law-enforcement officials, federal drug agents and others estimate. Even stepped-up federal drug enforcement efforts in south Florida and in southern coastal waters have had only limited effect.

And use of marijuana, heroin, and cocaine appears to be growing, according to data from the National Institute on Drug Abuse.

If the growing illicit-drug business is to be slowed, most experts agree, there needs to be a combination of: (1) greater efforts to stop the growth overseas of plants used in the drugs; (2) even greater enforcement efforts in the US and along its coasts; (3) more success in convincing American users, especially among the young, to stop using the drugs. A minority of analysts calls for a different approach: legalization of some or all of the now-illicit drugs, comparing efforts to block their use to efforts to enforce prohibition.

The US is talking with drug-producing and so-called conduit nations, but so far with little evidence of results. Many of the drug-producing regions are in remote parts of nations, which have little control over those areas.

The Reagan administration has stepped up enforcement efforts in south Florida and now plans to copy those efforts by setting up a dozen task forces across the US. Most state and local police give the US Drug Enforcement Administration and Federal Bureau of Investigation high marks for their efforts in south Florida and welcome the new task forces. But, they say, enforcement alone is not enough. For every arrest made, for every marijuana ship caught, other smugglers and dealers are ready to step in.

Efforts to get users to stop taking drugs have few results that can be attributed with certainty to those efforts. But high school seniors have begun to use less marijuana, and their use of other drugs has apparently leveled off, surveys show. Parent groups have formed in almost every part of the US, studying the effects of drugs, lobbying against the legal sale of drug-related items, and trying to give school officials and young people information on the effects of drugs.