What do you do when crocodiles move in next door?

A crocodile population explosion has made many residents of this Australian city, capital of the Northern Territory, angry -- and careful. In recent months, increasingly brazen reptiles in and around the Darwin area have:

* Chased families from picnic sites.

* Attacked vacationers' small fishing boats.

* Pursued swimmers.

* Stopped construction work in Darwin's harbor when several crocodiles clambered onto-floating platforms and lay aboard them in the sun.

* Taken up residence in a river pool only a few hundred yards from a cluster of suburban houses.

Darwin, a city that has been largely rebuilt after Cyclone Tracy flattened much of it in 1975, prides itself on its modernity.

But the citizens are equally proud of the Northern Territory's rough, tough image. Car number plates bear the slogan, "Outback Australia."

The most natural response, in this steamy, tropical city, would be to grab a gun and shoot the thick-skinned reptiles. But to do so in the "top end" -- as the territory is called -- is against the law.

The Northern Territory government has strictly enforced animal conservation rules protecting the crocodile, which is regarded as a threatened species.

Many locals don't agree. They maintain that protection has resulted in a population explosion that threatens the safety of humans.

Northern Territory Chief Minister Paul Everingham acknowledges that crocodiles, in the past year, have been responsible for two deaths -- a low figure considering the number of encounters.

Many Darwin residents have stories to tell of narrow escapes from crocodiles. Some of the tales are true.

One fatal incident in the territory involved an Aboriginal woman. She had been swimming with friends until a croc pulled her under.

The government's policy is, rather than sanction shooting, to earn revenue and create work by farming the crocodiles. So, when complaints are heard about crocodiles in the harbor or at picnic sites, game rangers round up the reptiles and use them to stock lagoons, situated in fenced areas.

The territory's government is currently considering applications to operate a crocodile farm on a site where it has stocked a lagoon with captured crocodiles.

The site and crocodiles will be supplied by territorial authorities. But all the necessary operating capital -- about $850,000 -- will be supplied by the company selected to run the farm, which will pay royalties once the farm is productive. If the first farm is successful, the administration will turn over other stocked lagoons to would-be crocodile farmers.

One wildlife protection rule the farmers will have to obey is that captured wild crocodiles, used for stocking lagoons, cannot be killed. They must be used only for breeding puposes. It is legal to kill crocodiles born in captivity, however.

Bob Young, spokesman for the Northern Territory Development Corporation, a government agency, says research has indicated a growing demand for crocodile skins."Asia will be the main market," says Mr. Young. "Hong Kong, Japan, Singapore, South Korea, and Taiwan need crocodiles and skins mostly for shoe and purse manufacture."

The government-assisted project will use saltwater crocodiles, a variety found along the Northern Territory coast both in fresh and salt water. They grow to about five yards in length.

However, several Northern Territory farmers plan to go it alone without government help. One poultry breeder has already started up his own crocodile farming project, using both saltwater crocs and another variety, the Johnston River crocodile.

The poultry breeder, Malcolm Eardley, has begun stocking his farm. His and the government-assisted project are expected to begin exporting skins in 1985.

Mr. Eardley says that by 1985 he will be breeding 4,000 crocodiles on his farm near Winnellie, 25 miles from Darwin. They will be fed o n tough old boilers from his chicken sheds.