The allegations date back to 2011 when the brothers were accused of posting disrespectful material online.
They fled the country and were on the run for four years, however they were later arrested when they returned home.
Both brothers have been in District Jail Jhelum since 2014.
Qaisar has three children with his wife Amina while Amoon is married to Huma who is a teacher at the Cathedral School, Lahore.
Their case was heard on December 13 by the Additional Session judge Javed Iqbal Bosal, who found them guilty and sentenced them to death.
The case was heard inside the jail due to security reasons.
The Centre for Legal Aid, Assistance and Settlement (CLAAS) is pursuing their case.
CLAAS has decided to challenge the decision as soon as possible. It claims in blasphemy cases the judges always remain under threat from religious fanatics and that is why the trial judges convict those accused of blasphemy.
Nasir Saeed Director of CLAAS, said: "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"
"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."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.