They deny any wrongdoing, saying the charges are politically motivated.
Mr Sharif, 67, resigned as prime minister in July after the country's Supreme Court disqualified him over undeclared income.
The court also ordered the National Accountability Bureau to investigate and conduct a trial into the Sharif family's wider finances.
Mr Sharif returned to Pakistan from London on Thursday after weeks of speculation. He had been staying in the UK capital while his wife underwent cancer treatment.
On Friday morning, the former prime minister, his daughter Maryam and his son-in-law appeared in Islamabad's accountability court.
But proceedings were adjourned shortly afterwards, as the accountability court had not received an order passed on Thursday by the Islamabad High Court.
What are the allegations?
They stem from the 2016 Panama Papers dump linking Mr Sharif's children to offshore companies.
They revealed that three of them owned offshore companies and assets not shown on his family's wealth statement.
The companies were allegedly used to channel funds to acquire foreign assets, including some apartments along Park Lane in London's Mayfair area.
Despite documents from the Panama Papers suggesting that the beneficial owner of the luxury central London flats was Mr Sharif's daughter Maryam, she later claimed that she was only a trustee - and that it was her brother who was the beneficial owner.
To prove her point, Maryam Nawaz produced a trust deed signed by both her and her brother dated February 2006.
But a British forensic expert later said the document was "fake" or had been "falsified" because it was typed in the Calibri font, which was not commercially available until 2007.
The insinuation that the offshore companies were meant to hide or launder ill-gotten wealth or to avoid taxes called Mr Sharif's credentials into question.
Mr Sharif, who in July was serving as prime minister for a record third time, was less than a year away from becoming the first head of government in Pakistani history to complete a full term in office.
He held the office from November 1990 to July 1993 and from February 1997 until he was toppled in a bloodless coup in October 1999.
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