The companies accepted climate change posed a challenge, and that New Zealand should transition to a lower carbon future. But they say Smith's claims were legally untenable and applied to strike them out.
The Supreme Court - the country's highest court - will consider whether his claims are clearly untenable and should not be allowed to proceed to trial.
Because of issues raised in the appeal, the court has granted consent to the lawyers for Climate Action NZ, Te Hunga Roia Maori o Aotearoa / The Māori Law Society and the Human Rights Commission to provide submissions.
The three-day appeal begins in Auckland on Monday.
In earlier appeals, Smith contended too little was being done in the political sphere on the issue of climate change, and called for a bold response from common law through the court.
The seven New Zealand companies were all involved in industries that either emit greenhouse gases or produce or supply products which release greenhouse gases when they are burned, he said.
These activities, Smith said, contributed to dangerous anthropogenic interference with the climate system and led to adverse climate events.
He said poor and minority communities would be disproportionately burdened by these adverse effects.