"Dear Madame," the letter from the West Coast couple in the United States begins, "we have been seriously trying to adopt an infant or young child for several years.

"We are not particular as to where the child comes from or how it comes to us. Our only preferences are that it is a healthy male between the ages of zero to three or four years of age."

The letter, attached to a color snapshot of a smiling couple with three youngsters, concludes that there are interested only in "legal" adoption.

The private agency social worker here who received it said her office gets at least 20 such U.S. appeals for Guatemalan children each month.

In other Latin American countries such as Colombia and Mexico, with well-organized private and government adoption channels, the monthly inquiries run into the hundreds.

The number of available U.S. children-especially the newborn, white and healthy ones who are most often sought-has diminished to the point where even the most desirable potential adoptive parents may have to wait years for a baby.

For those with the right information, or right connections, a child can be legally adopted in Guatemala and taken to the United States in two months to a year. Some willing to do it illegally, for a black market fee of $1,000 to $15,000, have received a child within days.

According to the U.S. Immigration and Naturalization Service, more than 1,000 Latin American children entered the United States legally for adoption iin 1977. "A lot" entered illegally, said an INS, "baby smuggling" investigator in Washington.

The technicalities follow a similar pattern in most Latin countries. In Guatemala, both legal and illegal babies generally through either private local attorneys specializing in the baby trade, or provate child care institutions, most of which are run by Americans.

Many of the illegal entries are made through Mexico by brokers who simply drive across the border with a new baby.

"On a busy day," the investigator said, "you could pass through Tijuana with a child in the car and say "it's mine' and be let through." INS is currently investigating baby-smuggling rings in both Mexico and the Orient.

The problems with such children begin when they need birth certificates or other identifying documents. Sometimes the problems start even earlier.

One such case, taken from the files of a registered child care and adoption agency here, involves an American couple who received a Guatemalan child two years ago.

"The child was from a domestic who lived in the house of a lawyer," an agency social worker said. "The couple got in touch with him, I don't know how, and paid the lawyer and his wife approximately $15,000 to bring the child to them. They also paid all their expenses, and paid for an interpreter since he didn't speak English."

More than a year after receiving the child, the couple got a call from the lawyer demanding more money on threat of exposure to INS.

"The woman was frantic," the worker said "She was afraid they were going to take her baby away."

The files give no indication of the resolution of the case, but the couple was obviously unaware of the usual INS attitude on discovery of a black market child already living in an adoptive home. The investigator said, "We'd check the home and make sure it's a good home," and then probably adjust the child's status to a legal one.

"We believe [smuggling] is done a lot," he said, "but when we find them, what are we going to do-take a child out of a parent's arms?"

Only two of at least a dozen children's homes operating here, however - the government facility and an American-run group - are registered with the Guatemalan government to arrange adoptions. The rest-almost all American-run-are allowed to operate primarily because there is no law that says they cannot.

Nearly all the unregistered facilities have opened since an earthquake devastated parts of Guatemala in 1976 and triggered publicity about homeless children. None is officially in the adoption business, but informed sources here say all of them have handled adoptions.

Many Guatemalan child care and adoption workers resent the American programs because of the lack of supervision. Despite what some of them say in soliciting funds in the United States, the Guatemalans said, the agencies house primarily children with families rather than orphans.

Some of the mothers who give up their children to the homes' care, one Guatemalan social worker said, might not if the facilities were less available.

Some homes seek candidates. They may find a pregnant maid who "wants to make her employers happy, and they may not want the child in the house. Maybe she is offered money," the social worker said.

"In general, though," she added "the babies come from low-income families, usually with only a mother. Some are abandoned in hospitals or in a village."

There is a feeding that the agencies sometimes are set up to help American consciences or needs rather than Guatemalan children.

Adoptive parents, the social worker said, either can't get a child in the United States, or "think adopting a foreign kid is the biggest good deed you can do."

But there is little denying the abject poverty of many Guatemalan families, and the snapshots on the office wall of Louise Gonzalez-an assumed name, used at her request-show both American parents and Guatemalan babies smiling with happiness.

Gonzalez, an American, and her husband, a Guatemalan lawyer, have been handling legal private adoptions here for several years.

"I do an average of two per month," she said, and the adoptive parents are charged only her expense and those of the natural mother.

One Maryland couple last year received two infants from Gonzalez-the children of unwed Guatemalan restaurant workers.

"They're bautiful babies," Mrs. Ray Merritt said. "We tried six or seven years ago" to adopt in the United States." Merritt has threee other foreign adopted children.

Merritt said they picked up their two new children in Guatemala "just before Thanksgiving. Now, we'd like one more." CAPTION: Picture 1, 2, These youngsters are being cared for by a private agency in Guatemala City. Many children are available for adoption, triggering intense interest in the United States, where demand for adoptions is high. Photos by Karen DeYoung-The Washington Post