NASHVILLE — A trial was to begin Tuesday in federal court that will determine what country will decide the fate of two 13-year-old twin boys at the center of an international custody battle that extends from Eastern Europe to Middle Tennessee.

The trial won't determine whether or not the boys should stay in Tennessee with their father or live in Eastern Europe with their mother, said John Crouch, an Arlington, Va.-based family law attorney who is not involved in the case. The question before U.S. District Court Judge Kevin Sharp is what country gets to decide that matter — Hungary, the U.S. or possibly Romania.

The boys are American citizens who were born in Texas, but have spent the majority of their lives in Hungary, court records show. Their father is an American with family in the Cottontown community of Sumner County. Their mother, a Romanian national with U.S citizenship, has invoked an international treaty claiming the children are being wrongfully retained in Tennessee by their father.

The boys came to Tennessee last year to visit their paternal grandparents in Sumner County for the summer. The father, who was supposed to bring them back to Europe, stayed in the U.S. and filed for divorce.

Whether the mother consented to have the children stay in Tennessee and enroll in school — even temporarily — is a question that could decide the outcome. She has sought the help of the U.S. State Department to get the boys returned to Europe.

Lawyers representing the parents in the trial in federal court in Nashville did not respond directly to messages seeking comment.

However, Couch, an attorney who works on international custody disputes says these kinds of cases are often very complicated, costly and can lead to financial ruin for some of the parents.

"A lot of these cases have tricky head-scratching issues," Crouch said.

The parents, Oana Olson and Oliver Olson were married in Romania in 1996, court records show. Their children, Spencer and Luca Olson, were born in Texas three years later. The family moved to Hungary in 2004 so the mother could go to dental school, and they stayed there until the summer of 2012.

The boys were living in Hungary when they went to visit their grandparents in Sumner County last summer. While they were away, the parents moved from Hungary to Romania, court records show.

The father, who was supposed to bring the boys back from Tennessee, wound up staying and filed a petition for divorce in Sumner County that asked that he be given primary custody of the boys. Oliver Olson has argued that the mother had threatened to divorce him when he returned to Europe because he no longer had a job in Romania, and he said he feared that he would not see the boys until they were 18.

It's not clear whether the boys want to stay in the U.S. The father has argued in court documents that their primary language is English, they are happy in Tennessee and surrounded by extended family.

The mother has argued that the father is in violation of a Hague Convention treaty designed to keep parents from illegally retaining children in another country. She maintains in court documents that the children miss Hungary, but she has also argued that parents shouldn't be allowed to wrongfully retain children in another country and then turn around and argue that the kids have gotten acclimated to their new surroundings. To do so, she argues, would only encourage parents to wrongfully abduct kids and take them to another country or illegally retain them in another land.

One of the central issues is going to be what country is considered the "habitual residence" of the boys. The mother maintains that it is Hungary. The father has argued that they had already moved to Romania, but the kids had not yet made the move.

The court is also being asked to determine whether the mother consented for the children to remain in Tennessee and enroll in school. If she consented, it could trigger the court to decide the preference of the boys, Crouch, the outside attorney, said.

Sharp has not yet decided whether the boys will be allowed to testify about where they want to live.

Regardless of what happens in federal court this week, the lawyer said, this is just the beginning of a long and costly court battle.