Lawyers representing Family First have been arguing why it should remain a charity.
Last year, the High Court upheld a decision by the Charities Registration Board to deregister the lobby group as a charity.
The High Court said Family First's promotion of traditional family values was not charitable work.
However, the lobby group doesn't accept that and has taken the case to the Court of Appeal.
The group's lawyers spent a lot of time today going over the High Court decision.
The issue of whether an organisation - which advocates and educates - can then be described as a charity - was also raised.
The matter before Justices Clifford, Gilbert and Stevens is set down for two days.