Qasir and Amoon are said to have posted disrespectful material on their own website, after which they fled Lahore for four years but then returned.
Their case was heard by the Additional Session judge Javed Iqbal Bosal on 13th December inside a prison due to security reasons and he found them guilty and sentenced them to death.
Both brothers have been in District Jail Jhelum in Punjab province since 2014.
The two men are both married and Qaiser has three children.
The UK group CLAAS (The Centre for Legal Aid, Assistance and Settlement) has decided to challenge the decision before the Lahore High Court Bench as soon as possible.
In blasphemy cases the judges are often under threat from religious fanatic, meaning trial judges frequently convict those accused of blasphemy.
Nasir Saeed Director of CLAAS-UK, said in a statement: "This is a very unfortunate situation as because of threats from hardliners lower courts pass their responsibility to the higher court and then it takes years to prove the accused innocent.
"We have seen this in the recent case of Asia Bibi, who was similarly convicted by the lower court and it took her years to reach to the supreme court to get justice. I am afraid now Qasir and Amoon will have to wait years to get justice.
"It is a sad reality that the present government has no intention even to talk about or to take steps to stop the ongoing misuse of the blasphemy law.
"Pakistani President Dr Arif Alvi has already said that the government would not amend the law. This means the killing of innocent people will continue despite growing opposition to the law around the world.
"While Imran Khan who has earned much appreciation from the world for his recent decision of opening the Kartarpur corridor for Indian Sikhs has no plans for Pakistan's own minorities, who are already scared of his reiterated statements of making Pakistan a Medina like state.
"Very recently his statement that there is no mention of Jesus in history, hurt the feelings of Christians not just in Pakistan, but throughout the world."
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