MOSCOW (AP) _ Lynn Wetterberg came to Russia hoping to adopt a child. But the Chicago accountant quickly discovered Russians want to give up only children nobody else will take.

''At the adoption center, they told me there may be a problem because my son is healthy,'' Wetterberg said angrily. ''And they said that healthy children are not allowed to be adopted by foreigners no matter what age.''

Americans who are fed up with waiting years to adopt an American baby - and who want to rescue a child from what could be a lifetime of economic misery - are turning to Russia. The Communist rulers of the former Soviet Union made it almost impossible for foreigners to adopt Russian children.

A U.S. Embassy consular official, who spoke on condition of anonymity, said 35 visas were processed all of last year for Soviet orphans, while 26 already have been processed in the first seven weeks of 1992.

But like Wetterberg, who adopted a daughter from Romania last year, many find the process far from easy. Many also learn that only children Russians don't want - those who are either mentally or physically handicapped or non- white - are available to foreigners.

The stigma of adopting a disabled or non-white child is so great in Russia that such children usually spend their entire childhoods in institutions.

''When I went in to the adoption center, the first woman told me there was no way I could adopt a healthy child, period,'' Wetterberg said.

She said later she was offered a healthy black baby. The majority of black children in orphanages are born to African fathers who come for college and Russian mothers who give them up because of the stigma.

Wetterberg eventually found a healthy 7-year-old white boy. She thinks the adoption is going through because of the boy's age.

''We try to give away children that wouldn't fit in with Russian families, children who are missing some fingers or missing a hand or something,'' said Alla Zugayeva, at the Committee for the Social Protection of Childhood in the Russian Education Ministry.

Zugayeva said Russia has no agency to deal specifically with foreign adoptions, and her committee fears people from overseas may start arriving in droves.

''We are very worried that we might be facing the Romanian situation here because we have no good controls right now,'' she said.

After the fall of Romania's Communist dictatorship, Westerners flooded into that country seeking to adopt orphans. A black market in baby selling sprang up, leading the government to suspend adoptions by foreigners while stricter rules were enacted.

Eight U.S. agencies that charge high fees to arrange adoptions are now operating in Russia, according to the newspaper Komsomolskaya Pravda.

''A Soviet baby on the Western or American market costs from $10,000 to $50,000 on up,'' the newspaper said Tuesday. ''But the children must be healthy with a twinkle in their eyes and be less than a year old.''

Phil Edelen, who also adopted a child last year in Romania, came this month to take two new daughters home to Park City, Utah. He avoided the American adoption agencies.

''All the agencies care about is money,'' he said.

Edelen said he decided to adopt a Russian after reading about the deteriorating economy and lack of food. He said he was thrilled with his baby girls, both of whom are mildly handicapped.

''My mission from God is that if we don't help the children, we don't have a future. I'd adopt everyone here if I could,'' he said.

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