How might John Wayne settle this dispute?

The heirs of John Wayne and a certain North Carolina university are duking it out over their right to the word “Duke.”

John Wayne Enterprises, a Newport Beach-based corporation that brands products — including alcohol — with the nickname of the legendary actor and Southern California denizen, alleges in a complaint filed last week in federal court that Duke University has been trying for years to block its use of the name.

On at least three occasions since 2005, the university has opposed attempts by John Wayne Enterprises to trademark the name, the document says.

Most recently, the university filed a notice of opposition to the company’s attempt to trademark an emblem that appears on a “Duke”-branded bottle of small-batch Kentucky straight bourbon — an image that also encompasses a stylized picture of the man himself, hat, gun and all.

The university also opposed John Wayne Enterprise’s trademark of the word “Duke,” written in a blocky serif font, the complaint says.

Now, the document says, enough is enough.

To remove the “cloud” of an eventual trademark infringement claim, the company is seeking a judge’s official declaration that the dueling Dukes can coexist without diluting either of their brands.

John Wayne’s childhood dog, named Duke, inspired the nickname that would stick with him throughout his long career, the document says. In Newport Beach, which Wayne called home for years, a lounge at the Balboa Bay Club was called “Duke’s Place,” in honor of the actor, who died in 1979.

Duke University, the complaint says, “does not own the word ‘Duke’ in all contexts for all purposes.”

Furthermore, it adds, Duke has never “been in the business” of marketing alcohol. Therefore, bottles of the hard stuff bearing the word “Duke” are unlikely to be mistaken for school-sanctioned party fuel.

But university spokesman Michael Schoenfeld wrote in an email, “The university doesn’t object to the use of ‘Duke’ on alcoholic beverages, as long as it is clearly linked to John Wayne’s likeness.”

However, he wrote, Wayne’s estate wants the rights to the word with or without the star’s image attached.

“While we admire and respect John Wayne’s contributions to American culture, we are also committed to protecting the integrity of Duke University’s trademarks,” Schoenfeld wrote in a statement.

“As Mr. Wayne himself said,” the statement continues, “‘Words are what men live by ... words they say and mean.’”

Richard Howell, John Wayne Enterprises’ attorney, disputed Schoenfeld’s account.

He said the company has proposed “over and over” a kind of truce: a co-use agreement wherein the company will only use the name “Duke” in connection with John Wayne’s name, image or likeness.

In any case, Howell said, “I think an argument could be made that on a worldwide basis, people are more likely to connect the moniker ‘Duke’ to John Wayne than they are to Duke University.”

Reached Wednesday evening, Schoenfeld declined to comment further.

No court date has been set.