Until yesterday, the Solomon R. Guggenheim Foundation was trying, apparently without much success, to fill a no. 2 position: someone who would run the New York museum while reporting to the foundation’s director, Thomas Krens.

With the announcement yesterday that Mr. Krens will step down — and that the Foundation will hire one person to play both roles — the outlook has drastically changed. Running the Guggenheim’s international network of museums is not an easy job, but it could be very appealing to the right person. So who are the candidates? The person who seems to be on everyone’s short list is the director of the Hammer Museum in Los Angeles, Ann Philbin. Ms. Philbin has been at the Hammer since 1999; prior to that, she was the director of the Drawing Center in New York. She is credited with transforming both institutions into vibrant centers for contemporary art.

Through a spokeswoman at the Hammer, Ms. Philbin said that she was flattered to be mentioned as a possible candidate but was “very happy here at the Hammer and in Los Angeles.”

The president of the Guggenheim Foundation, Jennifer Stockman, said in an interview that the search was not limited to people who were already museum directors, or to those with curatorial backgrounds. “We are honestly thinking outside of the box,” Ms. Stockman said. “Let’s not forget that when Tom became foundation director, he was a professor at Williams and had been involved in” starting the Massachusetts Museum of Contemporary Art. “It was a big leap for him.”

Ms. Stockman said that the board is not looking for someone to expand the museum’s global network further. “We want to get back to our mission of being first and foremost an art museum,” she said.

Another potential candidate is the director of the Los Angeles County Museum of Art, Michael Govan, who came to the Guggenheim as Mr. Krens’s deputy director and protégé when he was only 27 years old. Mr. Govan went on to run the Dia Center for the Arts and to establish Dia:Beacon. But he may not be ready to leave LACMA, where he just opened a new contemporary art wing, called the Broad Contemporary Art Museum. The director of the Wexner Center for the Arts at Ohio State University, Sherri Geldin, and the director of MassMoCA, Joseph Thompson, have also been mentioned as possible candidates. As for people who have not been directors, the chief curator of the Los Angeles Museum of Contemporary Art, Paul Schimmel, is a respected figure in the art world, as is the Whitney’s chief curator, Donna De Salvo.

Potential international candidates include the former deputy director for contemporary art at the Georges Pompidou Center, and now an official in the French Ministry of Culture, Bernard Blistène, and the chief curator of the Tate Modern, Sheena Wagstaff. The Guggenheim could also try to lure away the Tate’s director, Nicholas Serota.

An “out-of-the-box” candidate would be Samuel Keller, who until recently ran Art Basel and Art Basel Miami Beach, and is now the director of the Beyeler Foundation in Basel.

Olga Viso would be a good candidate, but she just took over at the Walker Art Center in Minneapolis. Meanwhile, her predecessor there, Kathy Halbreich, is settling in at the Museum of Modern Art. The undersecretary for art at the Smithsonian Institution, Ned Rifkin, is of Ms. Halbreich’s generation and may not be interested in running another museum.

Several people interviewed said that the major challenge facing the new director of the Guggenheim would be fund-raising. The Guggenheim’s endowment of $118 million is roughly twice its operating budget. By contrast, MoMA’s endowment is more than five times its operating budget.

Lisa Dennison, who stepped down as director of the New York museum last summer, to go to Sotheby’s, said in an e-mail that she did not regret the move. “I’m very happy with my decision,” Ms. Dennison said.

Mr. Krens’s departure means that two major international searches for museum directors are now underway: the Guggenheim’s and the Metropolitan Museum of Art’s. The searches are being handled by the same small company, Phillips Oppenheim.

Ms. Stockman said that the board had discussed the issue with Phillips Oppenheim and was not concerned about the overlap. “We think it’s going to be very clear who’s the right person for the Guggenheim and who’s the right person for the Met, and they won’t be the same individual,” she said. “But the fact that there’s going to be a shared reservoir of all these contacts and résumés will be helpful to both institutions.”