Dubai-based businessmen Kamal and Mohamed Eldarat have been in detention since August 2014, accused of involvement in the Libyan civil war.
Amal Eldarat, Mohamed's sister, said while the family was overjoyed a judge had acquitted her father and brother, they were concerned the men were not immediately released from custody.
"After the verdict, my dad and bother were taken back to prison," she said in a conference call. "We are disappointed that state security did not go with the judge's decision to let them go back to their homes."
Amal Eldarat quoted U.S. officials in Abu Dhabi as saying it could take a few days of administrative process for the men to be released.
"There have been some instances where people could take weeks or a month or a day," she said. "They are in desperate need of medical attention."
Family members and human rights groups alleged the two men were tortured while in custody. UAE officials said the pair were accorded "due process" and treated "in accordance with international fair trial standards."
Greg Craig, the U.S.-based lawyer for the men, credited the Obama administration and consular officials with being "appropriately and energetically" concerned, especially at working behind the scenes and assisting with health concerns.
"Ambassador (Barbara) Leaf was also very involved. We know the White House was also very involved," Craig said. "Without their support, we wouldn't have had the attention this case got."
Man and son arrested after UAE joins U.S. in airstrike on Libya
Real estate developer Kamal Eldarat and his 34-year-old son Mohamed, who runs a Subway sandwich franchise, were arrested in August 2014
at their home in Dubai.
Kamal fled his native Libya during Moammar Gadhafi's reign more than 25 years ago, moving his family to California before settling in the UAE in the 1990s, Amal Eldarat said.
The Eldarats were among a group of Libyan businessmen rounded up just days after UAE and Egyptian planes launched airstrikes against Islamic militants fighting in Libya's civil war. The Eldarats deny supporting the two militias, which the UAE contends are linked to terrorism.
The UAE has become more aggressive in fighting Islamic militants since the 2011 Arab Spring sparked revolution across the Arab world, particularly the Muslim Brotherhood. The two militias the Eldarats were accused of funding -- Libya Dawn, and the February 17 Martyrs Brigade, which was once hired to protect the U.S. consulate in Benghazi -- have ties to the Muslim Brotherhood.
Neither are designated terrorist groups by the United States or the United Nations, but February 17 has been linked to Ansar al-Sharia, which has ties to al Qaeda and which the United States does consider a terrorist group.
Family and U.N. see evidence of torture
Amal Eldarat said her father and brother were held incommunicado in a remote desert prison for months and were subjected to electric shocks and to a mock execution. Later they were moved to a regular prison and forced to confess ties with the militia groups, she said
In January, more than 16 months after their arrests, the Eldarats were charged under a terrorism law enacted after their arrest.
In February, the United Nations special rapporteur on torture cited "credible information" the Eldarats and several other Libyan detainees "were tortured and forced to sign confessions."
Eldarat said her brother has lost hearing in one ear and her father, who suffers from acute back pain, has lost tremendous weight.
"My dad was like a walking skeleton," she said of her last visit with him. "It was like he was gone."