However, the Council has denied the board was obliged to offer to sell the land to the families under the Act.
It says the land was not, on the coming into force of the Act, held for any public work, but alternatively, if it was, it was held for various public works purposes.
In the latest action, the seven plaintiffs took the council to the High Court at Auckland last year, to fight for the land to be returned. The council raised nine objections during this hearing.
The first eight were thrown out, however the seven plaintiffs lost their claim based on one point.
In the High Court decision from last year, Justice John Fogarty said the Auckland Harbour Board and Waitemata City Council Empowering Act 1983 ended the board's obligation to offer back the land to them.
Under the Empowering Act, the Public Works Act had no application to the land.
The long-running case is now before the Court of Appeal, with one of the plaintiffs, Charles Williams, appealing against the High Court decision.
Speaking at the Court of Appeal today on behalf of Auckland Council, Matt Casey QC, said that by 1982, the council was not holding the land for public works, but for industrial development.
He said the abandonment of any port proposal for the land, meant it was no longer required for that public work purpose.
If that was the case, the council was not obliged to sell the land back to the families.
Furthermore, Mr Casey argued the plaintiffs had been aware for some time that the board was not planning to use the land for port purposes.
The hearing, before Justices Harrison, French and Mallon, is set down for two days.