Story highlights The state says it will appeal the judge's ruling

But how much luck it will have remains to be seen

Five gay couples sued the state in May to overturn the ban

Sunday's ruling is yet another victory for supporters of same-sex marriage

(CNN) In 1998, Alaska became the first of two states to pass a constitutional amendment to ban same-sex marriage.

On Sunday, a federal judge overturned the 16-year ban, saying the Constitution guarantees equal protection to all.

The judge's ruling makes Alaska the latest state where gay and lesbian couples can legally marry.

"The plaintiffs in this case do not ask the court to recognize an entirely new fundamental right to same-sex marriage; rather, plaintiffs wish to participate in the existing liberty granted to other couples to make a deeply personal choice about a private family matter," U.S. District Judge Timothy Burgess wrote in his 25-page ruling

Alaska says it will appeal.

Read More