The two asylum seekers, identified only as plaintiffs M61 and M69, arrived by boat in 2009, reaching Christmas Island on October 2.
Both claimed refugee status out of fear they faced persecution from the Sri Lankan army, agencies of the government and paramilitary groups because of their alleged support for the Liberation Tamil Tigers of Eelam.
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Both were assessed by an official from the immigration department before their asylum claims were rejected.
A review, conducted by a firm contracted by the federal government for Christmas Island cases, upheld the decision.
Faced with deportation, the pair appealed to the High Court on grounds of lack of procedural fairness because Immigration Minister Chris Evans had failed to personally consider their cases.
The case for the two Tamils is being argued by the Refugee and Immigration Legal Centre.
Executive director David Manne says the centre is challenging the fairness of offshore processing.
"The government's position is that under its offshore processing regime, unlike on the mainland, a court can't look at whether the decisions on these life-or-death matters were made fairly or lawfully," he told ABC Radio on Tuesday.
"But our clients are also saying that in this context that a fair and lawful process should be applied in the same way that it is for people who arrive on the mainland."
