Bakery owners the McArthur family said: "After much careful and prayerful consideration given to legal advice, we have decided to appeal the judgment handed down last Tuesday.
"We continue to insist that we have done nothing wrong as we have discriminated against no individual but rather acted according to what the Bible teaches regarding marriage.
"As many other people have already noted, Christian beliefs seem to have been trampled over in this judgment and we believe this only has negative effects for our society."