P operates a large chain of grocery stores in Mexico, called 'Gigante.' P registered the 'Gigante' mark as a trade name in Mexico and has kept its registration current ever since. Two of its stores were in Tijuana, a city on the U.S.-Mexican border, just south of San Diego. In August 1991, D began operating a grocery store in San Diego, using the name 'Gigante Market.' A second store was opened in 1996. In 1995, P began exploring the possibility of expanding into Southern California. It learned of D's Market in San Diego. P decided against entering the California market at that time. In 1998, P arranged a meeting with D in June 1998 to discuss D's use of the name 'Gigante.' The meeting failed to resolve the mark issues. In June 1998, P registered the 'Gigante' mark with the state of California. D did likewise in July 1998. Neither has registered the mark federally. In May 1999, P opened its first U.S. store. That store was followed by a second later that year, and then by a third in 2000. All the stores were in the Los Angeles area and all were called 'Gigante.' D sent a cease-and-desist letter. P filed this lawsuit. The court recognized that under the 'territoriality principle,' use of a mark in another country generally does not serve to give the user trademark rights in the United States. But it held that because P had already made Gigante a well-known mark in Southern California by the time the d began using it, an exception to the territoriality principle applied. Under the 'famous-mark' or 'well-known mark' exception P's earlier use in Mexico was sufficient to give it the superior claim to the mark in Southern California. P was entitled to a declaratory judgment that it had a valid, protectable interest in the Gigante name but laches barred P from enjoining D from using the mark at their two existing stores. Both parties appealed.