A monkey in a phone booth. A silver fox in a hotel. A goat, a pony, a snake, a wildcat, a baby owl - the Washington Animal Rescue League has retrieved all those animals from downtown streets.

Those animals may have been the most unusual cases. The 12,000 to 15,000 injured, lost or unwanted animals the Rescue League helps each year usually are the more familiar family pets - dogs and cats.

The Rescue League, a non-profit organization, functions primarily as an adoption agency. But the league also provides other services. Its new premises at 71 Oglethorpe St. NW include the Tailwagger's Clinic - and independent, outpatient veterinary center, which has a lost and found facility, an information bureau and a classroom where District school children are instructed in the humane treatment of animals.

"Placing animals in safe and responsible homes is our overriding concern," said Elizabeth Kiernan, president and lifetime member of the league.

"If no one wants the animals after at least five days, space limitations make destroying some of them necessary. Animals deemed adoptable by staff members are kept as long as possible. It's not a happy life, anyway, to stay kenneled with no home or owner."

Sometimes staff members decide they simply can't destroy certain animals, and bringing unwanted animals home is not uncommon. For example, Kiernan says she has "only" two labrador retrievers, but she owned five a few years ago.

And take the case of Remus, the league mascot.

"Remus is a bull terrier with a terrible skin condition. He has practically no fur. No one can adopt him because he has a habit of killing other animals," Kiernan said. "But he's got an appealing personality, so we keep him around."

Overpopulation continues to be the major problem facing people concerned with the welfare of animals. Kiernan said she can't understand why people insist on breeding their pets, especially when she sees the results at the Rescue League kennels.

"Even purebred dogs, worth a great deal of money, are turned into the shelter because suitable homes can't be found." she said. "Overpopulation is a serious threat everywhere, not only in Washington. The old formula of the pound capturing animals, bringing them in and killing them hasn't been effective. Most people informed about the care of animals have concluded that birth control is the only solution.

"Without exception, our policy is that every female pet gets spayed, and every male cat neutered, within 10 days of placement into a home."

When the pet's owner can't afford to pay for the operation, the league subsidizes the cost.

The league has been protecting animals 24 hours a day, for the past 64 years. Its budget of more than $150, 000 a year is funded by donations, private endowments and life memberships. The league has a staff of 12 fulltime and part-time employes and operates two ambulances.

The league has been in new facilities on Ogethorpe Street since last October. The building has a kennel with 46 runs, rooms for wildlife and for bitches in whelp, three kitchens and two grooming rooms.

To prevent infections, dog and puppy runs are separated, and stray cats are kept apart from other cats and kittens.

In keeping with the league's goal of providing healthy, clean and comfortable surroundings, a plan is under consideration to pipe soft radio music into the kennels to relax the animals, Kiernan said.

The 116-foot long skylight in the brick-walled reception room illuminates Albert Schweitzer's prayer for animals and brightens up the cases where adoptable animals are displayed.

The league is the only shelter of its kind in the metropolitan area. The D.C. Pound administers a public health and rabies control program, and the Humane Society concerns itself with preventing cruelty, Kiernan said.

Kiernan said she believes cruelty to animals can be averted through proper education.

"Cruelty occurs because people are ignorant or unthinking. Of course, there are some fiends who cut up animals and beat them or throw them out of windows, but they are in the minority."

The shelter is open to the public for tours from 11 a.m. to 3:30 p.m. weekdays and from 11 a.m. to 3 p.m. on weekends. The phone number is 667-5730.