There can evidently be only one Hotel California: music legends the Eagles have settled a lawsuit to stop a Mexico hotel from using the name "Hotel California," arguably the rock band's most famous song, after the hotel's owners withdrew their application to trademark the name in the United States.

A joint dismissal of the band's lawsuit against Hotel California Baja LLC, which runs the Todos Santos hotel in Baja California Sur, was filed on Wednesday with the US District Court in Los Angeles, Reuters reports.

"This case has been settled by mutual agreement of the parties," Thomas Jirgal, a lawyer for the Eagles, said in an interview on Thursday.

The dismissal came on the same day the US Patent and Trademark Office accepted Hotel California Baja's request to permanently abandon its trademark application.

Neither the hotel nor its lawyer immediately responded to requests for comment.

"Hotel California" is the title track from the 1976 Eagles album of the same name, and won the 1977 Grammy award for record of the year.

It is known for a long guitar outro by Don Felder and Joe Walsh, and abstract lyrics that lead singer Don Henley told CBS News in 2016 depict "the dark underbelly of the American dream."

Hotel California Baja was accused of wrongly encouraging guests to believe the Eagles authorized using the song's name, such as by playing the band's songs throughout its property.

The Eagles said this was done in part to spur sales of T-shirts, posters, refrigerator magnets and other merchandise for guests to take home after they check out and leave.

In court papers, Hotel California Baja denied it was trying to mislead guests, and said they were unlikely to be confused.

Located about 1,609km south of San Diego and 77km north of Cabo San Lucas, the hotel had been called Hotel California when it opened in 1950.

It underwent some name changes, but the original name was revived after John and Debbie Stewart, a Canadian couple, bought the property in 2001.