Intikhab Alam, former test captain, and barrister Shahid Hamid were among the tribunal members, with a report to release its findings to be delivered to the Pakistan Cricket Board (PCB) in two weeks time.
"The tribunal met for some three hours and both of them were questioned for an hour after which they left and the members carried on their deliberations," a board spokesman told Reuters.
"The tribunal is expected to meet again on the 26th," he added.
Nasim Ashraf, PCB Chairman, told reporters that the board would carry out the recommendations of the tribunal and would release the outcome to the public.
"We will not be taking any popular decision under pressure from anyone," Ashraf said.
"We will take a correct decision. The World Cup is important for us but more important is the image of the country. We will act impartially and fairly."
The PCB chief made it clear that Akhtar and Asif would be given a fair chance to defend themselves.
"A thorough independent investigation is being carried out. They have been accused of testing positive but we don't know if they took it inadvertently or intentionally.
"The players can now bring anyone before the tribunal in defence," Ashraf added.
The fast bowling duo face an immediate two-year ban if they are found guilty of doping.