Lacoste appealed this and was successful in the High Court, where Justice David Collins overturned the assistant commissioner of trademarks' decision.
Crocodile International then went to the Court of Appeal, with Queen's Counsel David Laurenson arguing Justice Collins was mistaken because he incorrectly identified the "essential elements" of Lacoste's trademark.
However, the Court of Appeal was satisfied Justice Collins' identification was correct, saying the crocodile image was the "central idea and message" of the logo, not the word crocodile or the combination of the word and logo.
"As we put it to Mr Laurenson, it is all about the crocodile," the appellate court said.
Crocodile International, this afternoon, was given leave to appeal to the Supreme Court.
The question the country's highest court will consider illustrates the long-winded nature of the dispute so far:
"Did the Court of Appeal err in upholding the High Court decision to set aside the order made by the Assistant Commissioner of Trade Marks revoking [the trade mark]?"