The Swiss branch of the Raelian religious sect on Wednesday asked the European Court of Human Rights to overturn a ban on the group's posters depicting aliens.
Authorities in the Swiss canton of Neuchatel in 2001 banned the group from putting up the posters, which also carried a web address and a phone number.
The sect was created in 1973 by Francais Claude Vorhillon, a Frenchman now calling himself Rael. The group claims aliens created life on earth.
Though authorities in other parts of Switzerland allowed the Raelians to put up the posters, officials in Neuchatel said the publicity presented a threat to public order because Raelians promote human cloning and "geniocracy," a system where leaders are picked according to their intelligence.
Authorities also pointed to ambiguities in Raelian statements on paedophilia.
Swiss high courts affirmed the ban and the European Court of Human Rights in January upheld the decision.
In an appeal on Wednesday, Raelian lawyer Elie Elkaim argued before judges that cloning is not illegal. He said the religious movement had repeatedly condemned all acts of paedophilia and said it was contradictory to ban a poster when neither the sect nor the website are barred.
"It's one thing to visit the website by chance or through personal interest, but another to attract the attention of a wider audience," said Frank Schurman, lawyer for the Swiss authorities, highlighting "a real problem with the sexual proclivities of some (group) members."
The Raelian movement claims tens of thousands of members worldwide.
Rael says life was created on earth 25,000 years ago by aliens, which he claims to have met.