The two, along with fast bowler Mohammad Asif, were provisionally suspended by the Iinternational Cricket Council (ICC) over allegations they were involved in spot-fixing during Pakistan's summer tour of England.
All three appealed, but Asif later withdrew his application. The two cricketers arrived with their lawyers - Salman with Khalid Ranjha, a former law minister, and Aftab Gul, a former Pakistan player, and Aamir with his lawyer Shahid Karim.
Both Salman and Aamir on Saturday, wearing casual shirts and trousers, waved to the media but did not speak as they entered the ICC headquarters.
The scandal broke after a report by British tabloid The News of the World prompted Scotland Yard to launch an investigation into allegations of spot-fixing during the Lord's Test against England in August.
Police raided the team's hotel in London and questioned Salman, Aamir, Asif and bowler Wahab Riaz, but they have yet to formally level any charges.
Owing to their suspensions, the trio have been excluded from Pakistan's current tour of the United Arab Emirates, where they are playing South Africa.
Michael Beloff QC, chairman of the ICC's code of conduct commission, will hear the appeal against the provisional suspensions and has the power to overturn them. The hearing will continue on Sunday. Salman and Aamir have vowed to clear their names.
"I am confident that I will be cleared and will be available to play for Pakistan soon. We have committed no mistake and the sting operation of the News of the World has flaws," Salman told AFP last week.
According to the ICC process, the matter of the players' code of conduct violation will not be heard during the current hearing. The ICC code stipulates a minimum five year ban if charges of corruption are proved.
The commission is expected to announce a decision on the players' appeals toda (Sunday) in a ruling that can not be further challenged.
Salman's lawyer Gul Friday said he expected a fair hearing. "We are going for justice in their court," said Gul, who played six Tests for Pakistan between 1969-71.
"We can't pre-empt what decision they give, it's their discretion, but our case is very good. There is no strong evidence against Salman on the basis of which we can say that he should remain suspended."
Pakistan Cricket Board said the players will be readily available if their provisional suspension is lifted.
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