By JANE PERLEZ

          WASHINGTON, April 24 -- In an immediate sense, the hostility
          in Cuban-American official relations is unlikely to be touched by the Elián
          González case. But in the longer term, the dispute could encourage trends in
          American public opinion that favor more relaxed ties, experts say.

          To change the relationship fundamentally, the trade embargo strengthened by
          Congress and signed by President Clinton in 1996 would need to be ended,
          an impossibility in an election year and in the current overheated atmosphere.

          If the Republican candidate, George W. Bush, wins in November, there is not
          likely to be a change in policy; nor is it clear that Vice President Al Gore would
          push for much change, particularly given President Fidel Castro's defiance on the
          question of improving relations.

          For their part, Clinton administration officials have repeatedly said there would
          be no change in policy toward Cuba because of a family argument over a
          6-year-old. The White House went out of its way to focus the drama as a legal
          one, not a matter between two nations.

          But subtle shifts in Congress and small tinkering by the Clinton
          administration on the travel ban to Cuba last year point to movements in
          policy and attitudes that the González case could propel in some ways.

          Close to 200,000 Americans, both legal and illegal travelers, visited
          Cuba last year, nearly double the number from 1998, according to Julia
          Sweig, the deputy director for Latin American affairs for the Council on
          Foreign Relations. According to the Cuban government, Americans now
          account for the second-largest group of visitors, after Canadians.

          "This is a lot more exposure to Cuba," Ms. Sweig said, noting that the
          American travelers ranged from Hollywood producers to Midwestern
          farmers looking for business selling seeds to nongovernmental agencies.
          (The farmers went under a new program sanctioned by the Clinton
          administration, but they found little business.)

          This exposure has contributed, Ms. Sweig said, to a "certain sense of
          exhaustion -- people are tired of deferring to a Cuban-American minority
          view."

          A Gallup poll last May showed that 70 percent of Americans were in
          favor of lifting the trade embargo against Cuba, with 28 percent
          opposed. More than 20 years earlier, another Gallup poll showed that 63
          percent favored abolishing the trade embargo and 37 percent were
          opposed.

          An ABC News poll conducted earlier this month, in the heat of the
          González battle, showed a shift in opinion, with respondents evenly split
          on whether to restore relations with Cuba and end trade restrictions.
          Respondents strongly favored removing travel restrictions between the
          United States and Cuba.

          In Congress, where opposition to improving ties with Cuba has been the
          most enduring, the Senate voted last year, 70 to 28, in favor of ending
          the restrictions on sending food and medicine to Cuba, a softening of
          attitude that took some by surprise.

          In the same vein, Congressional supporters of broader ties with Cuba
          noted that earlier in the Elián González dispute, Senator Robert C. Smith,
          Republican of New Hampshire, could not muster enough support in the
          Republican Senate caucus to give asylum in the United States to the
          child.

          The most passionate anti-Castro crusaders in the Congress nonetheless
          believe that in the short term, the heightened tensions stirred by the case
          have helped their efforts to slow any move to normalize relations. But
          others doubt that there will be any lasting impact.

          For example, in permitting more Americans to go to Cuba, the Clinton
          administration believes that it has broadened the debate within the United
          States and undermined somewhat the power of the Cuban American
          minority in Florida.

          Since last May, academics, artists, scientists and other professionals have
          been allowed to apply for licenses from the Treasury Department to visit
          Cuba; the departure points were expanded from Miami to include New
          York and Los Angeles. Many other people have gone illegally as tourists,
          administration officials said.

          The González case is important because it is "the first time, two
          governments find themselves on the same side of an issue," said Wayne
          Smith, who was the head of the United States Special Interests section in
          Havana from 1979 to 1982.

          It also served a purpose for policy in a human way. "The more Cubans
          are seen as normal human beings -- that the father is a decent guy --
          public opinion will swing," he said.

          The Clinton administration policy has been carefully devised, according
          to a former National Security Council official, to ensure that it was not
          "Castro-centric" but rather "people-centric."

          Richard Feinberg, who dealt with Cuba policy on the council in the early
          Clinton years, said the administration decided that there was not much to
          gain by directing a policy at Mr. Castro, who has consistently defied any
          attempts at relations with the United States.

          Rather, he said, the policy was devised to build up a civil society in Cuba
          so that in the "indeterminate time when the regime collapses, that there is
          not a vacuum and a transition to a peaceful society is much easier."

          Any Democratic administration would be reluctant to initiate dramatically
          changed relations with Cuba because Mr. Castro has been so
          unreceptive, Mr. Feinberg said.

          Among the changes that Mr. Clinton offered but did not achieve last year
          was a direct postal link between Cuba and the United States. An
          administration official said today that Mr. Castro rebuffed the idea.

          The administration was considering easing the travel restrictions further
          last fall but put the idea aside at the height of the González crisis. At the
          same time, there was a proposal to enlarge the remittance program,
          which was eased in January 1999 to allow American citizens to send
          $300 each quarter to family members in Cuba.

          At the United Nations Human Rights Commission in Geneva last week,
          the United States vigorously pushed the case against Cuba.
          Administration officials said they were pleased that a motion citing a
          deteriorating human rights situation in Cuba was passed by a larger
          margin than in the past.