The International Campaign for Human Rights, Physicians for Human Rights, and Human Rights Watch say they believe the accusations of plotting a coup are being brought unfairly, without the brothers being given a chance to adequately defend themselves.
The Alaei brothers have been in jail in Iran since June 2008.
Their trial was reportedly held in Iran about 10 days ago behind closed doors. Their sentences, and fates, are unknown.
The Alaei brothers had been carrying out HIV/AIDS treatment and prevention programs, particularly focused on harm reduction for injecting drug users. In addition to their work in Iran, the Alaei brothers have held training courses for Afghan and Tajik medical workers.
Rights groups have expressed outrage over their arrest and have called on Iranian authorities to release them.
Joe Amon, director of the HIV/AIDS and human rights program at Human Rights Watch, has said the case is another example of how “under President Mahmud Ahmadinejad’s administration, Iran’s human rights record has reached new lows."
(by RFE/RL correspondent Golnaz Esfandiari)