Responding to today's deadline under the Gramm-Rudman-Hollings act for cutting federal expenditures, the Smithsonian Institution yesterday canceled or delayed several shows and eliminated extended summer hours for the museums.

Such activities directly affecting daily visitors to the Smithsonian, however, account for about an eighth of the $8.6 million cuts that were made in the institution's budget. Research was cut by $1.7 million; collections by $1.3 million; and administration, buildings and "facilities management" by $3.4 million.

Smithsonian Secretary Robert McC. Adams said the organization "sought to minimize the impact on the public . . . The543389044however, inevitably affect all facets of the Smithsonian's federal operations.

"Although their effects may appear marginal since they are necessarily widely scattered, the impact on the contents of many programs will in fact be substantial," Adams continued. "Particularly vulnerable are innovative and experimental activities . . . Some of these, unfortunately, are precisely the activities that could contribuite most importantly to the Smithsonian's future strength and vitality."

The Smithsonian's announcement follows on the controversy raised by Librarian of Congress Daniel J. Boorstin's decision to meet the budget mandate by slashing hours in the library's general reading rooms byendcol sk one-third. And National Gallery of Art Director ld,10 sk,2 sw,-2 J. Carter Brown testified last week to a congressional committee that cuts of $1.58 million required in the federal part of his budget would eliminate extended summer hours at the gallery as well.

At the Smithsonian, cancellation and postponement of exhibits will save $500,000, and cuts in "exhibition-related support activities" will amount to another $500,000. The National Museum of Natural History will "delay completion" of a Paleobiology Complex, a permanent installation, and will "postpone or cancel a number of other exhibits or installations."

An exhibit called "Post Office Murals" has been canceled at the National Museum of American Art. An exhibit on the U.S. Patent Office has been "deferred" by the National Portrait Gallery. "A number of planned small exhibitions designed to enhance and update segments of major existing galleries" have been canceled at the Air and Space Museum. And at the Museum of American History, "a number of free public programs, including a variety of American music programs in April, May and June" have been canceled. The opening of "Engines of Change," a major installation at the history museum on the Industrial Revolution and its social impact, "will depend on securing adequate private funding," the announcement said.

Among the large Washington cultural institutions also affected by the budget cuts are the Kennedy Center and Wolf Trap Farm Park for the Performing Arts, both of which are maintained by the National Park Service.