Barrister Shahid Hamid chaired the tribunal which also included former captain and coach Intikhab Alam. Third tribunal member Waqar Ahmed, a doctor and doping expert, could not attend the meeting as his flight was delayed.
Akhtar and Asif were sent home from the Chammpions Trophy in India on Monday after their urine samples tested positive for the banned steroid nandrolone. Their 'B' samples are yet to be examined.
The pair reached Pakistan Cricket Board (PCB) headquarters at Gaddafi stadium early Saturday to record their statements separately.
"The hearing lasted around four hours as we had to do some initial work and then heard Akhtar and Asif. We have given them reports of their tests and have asked them to submit their written statements in the next hearing," Hamid told reporters.
The next hearing is scheduled to be held on October 26.
The tribunal is expected to take two weeks to return its findings and recommendations to the PCB, which will then take a final decision.
"I cannot predict any time frame but would try to reach the conclusion as early as possible. We will give fair chance to both the players and then submit our report to the PCB," Hamid said earlier.
Hamid said both players were briefed about the procedure of the case.
"Both Akhtar and Asif have been told about the procedure of the doping matters and have also been advised that if they want they can also bring their lawyers in the next hearing," said Hamid.
Under International Cricket Council doping rules, the penalty for a first doping offense is a two-year ban. However, the PCB said it will take its own decision since the tests were conducted internally.
Both Akhtar and Asif have pleaded their innocence, saying they have not deliberately taken any banned substance.
The PCB said that if both the players demand tests on their B samples, they would be given the opportunity once the tribunal work is over.