The Investigative Committee, which probes serious cases, said that Moscow social workers were suspected of criminal negligence for allowing the two boys to live in the family since 2010.
This is the first such case ever launched, reported Interfax news agency.
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"Nothing like this has happened before," said lawyer Maksim Olenichev of Vykhod (Coming Out) support group based in the northwestern city of Saint Petersburg.
He told AFP he was in talks with the family to represent them legally because "we think we need to defend this family from the actions of the state."
The charge could see the officials fined or sentenced to community service.
The case so far does not affect the family directly but if the officials are found guilty, "it could give the state the opportunity to demand the annulment of the adoption," Olenichev said.
"We think this is unacceptable as the family is established," he said, specifying that the boys are now teenagers.
Russia has banned adoption by foreigners from countries where gay marriage is allowed, but since legalised unions are not possible in Russia, there is no law banning adoption by a gay couple.
However the Investigative Committee accused the gay man who adopted the children of "propagandising non-traditional values" to minors, which is illegal under a controversial law that has been used as grounds to cancel public gay pride events.
"This is the next twist in that law," said Olenichev. A statement by investigators accuses the gay couple of causing the children to form "distorted ideas about family values, harming their health and moral and spiritual growth."
Lawyer Olenichev said however that a "psychiatrist told us the children are developing absolutely normally."
The law banning gay "propaganda" was passed in 2013, while President Vladimir Putin in the same year signed into law a ban on gay and lesbian couples from foreign countries adopting Russian children.
It also banned adoption by unmarried individuals who live in countries with laws permitting same-sex marriages.
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