Inside the first-floor State Department office of Alan G. Swan, one of the coordinators for the U.S. relief effort in Mexico, there is a large model of the Titanic.

Swan needs a sense of humor. Nine days after a giant earthquake ripped through Mexico City, Americans are still phoning his team at the Office of Foreign Disaster Assistance (OFDA), offering everything from drills and dogs to beds and bulldozers. The problem is how to explain that most are not required.

"We have had thousands of phone calls," said Swan, an assistant director at OFDA, "and we would like to express our deep appreciation . . . ." But he added that his team had been able to take up only a fraction of the offers.

Dealing with a generous but frustrated public, though, is perhaps the least of the tricky problems facing the disaster squad.

The problems range from the technical difficulty of coping with what Swan calls "a sophisticated urban earthquake" to the finer diplomatic point of how to help a proud nation, Mexico, which has always sought to keep a discreet distance from its neighbor to the north.

So far, the OFDA team, part of the Agency for International Development, appears to have kept its balance. "We are only responding to specific Mexican requests for assistance," OFDA Director Julius W. Becton Jr. said. Becton, a retired Army general, is in overall charge of the relief operation.

Becton recalled that after an earthquake in Guatemala last year, his office received a call from a citizen offering 1,000 high-heeled shoes. By Wednesday this week, the 38-member OFDA team had compiled a 13-page printout of more practical items either made available or shipped to Mexico City.

For example: 10,000 disposable oxygen masks from Memphis, 24 water tanks, 120 rolls of plastic sheeting, 20 oxygen bottles in a shipment from the Defense Department, acetylene torch equipment from the governor's office in Texas, body bags, two high-frequency radios and water trailers from Richmond.

Inside OFDA's main office, around a horse-shoe shaped table, there are 13 phone banks with round-the-clock operators. Aid comes free, or as in the case of a 10-strong doctor-and-nurse team from Mississippi, is for hire at $30,000 a week. Offers are logged by a team that has included an ambassador's wife, a State Department personnel manager and an OFDA water provision specialist who has spent the last few months working on the drought in Africa, still a big preoccupation for the agency.

In addition, military professionals such as Steve Boyce, an Air Force major, are responsible for first finding materiel and then coordinating shipment. There are 10 "consolidation points" around the United States for military airlifts; commercial flights are leaving "wherever planes are available," Boyce said.

Since he started work Monday, Boyce said, OFDA has been directly or indirectly involved in up to 50 such flights.

One of the more dramatic examples of the private and public sector working together on these flights came in the first hours after the earthquake. OFDA took a call from the California Rescue Dog Association, which was holding a convention in Nashville.

"We had a plane leaving from Pittsburgh so we stopped off in Nashville and flew on to Mexico City," Swan said. "The dogs were of real use to the Mexicans."

Other important examples of targeted support cited by Swan included a Dade County, Fla., Fire Department unit and a team from the U.S. Forest Service equipped with fire-fighting helicopters. However, an initial request from the U.S. Embassy in Mexico City for Sikorskys was rejected because they generate strong downdrafts that could topple unstable buildings in Mexico City.

Swan said the Mexico City earthquake was the agency's first major urban earthquake in its 20-year history. Most others had occurred in rural areas. "You are faced with complicated demolition, extraction and removal operations," he said. "We have to find new solutions to new problems."

In the next few days, Swan said, the relief effort would switch to cleaning up the city and focusing on public health hazards. If Mexico continued to request aid, he said, the agency was ready to offer all available expertise.