President Reagan may have his woes, but dissatisfaction with the executive is as old as the republic itself.

In the disputed election of 1876, for example, in which Rutherford B. Hayes was declared the victor, a citizen named Augustus Wilson proposed abolishing the Presidency itself. Not only would the election dilemma be solved, he wrote, but all future problems could be avoided. ''All are aware that republics have existed in all the ages without a single executive,'' he wrote. In that same year, the residents of Potter County, Pa., proposed an amendment to eliminate the Senate, complaining that it was ''aristocratic'' and had ''always advanced the interest of the money, railroad and manufacturing speculators to the prejudice of the common welfare.''

In 1893, Representative Lucas Miltiades Miller of Wisconsin proposed renaming the country the United States of the Earth, since, he argued, ''it is possible for the Republic to grow through the admission of new States into the Union until every Nation on Earth has become part of it.'' The resolution outlining the administration of this vast new nation has a provision that ''the House and Senate would vote by electricity.''

Most of the documents are in pristine condition, but one is wrinkled and smudged with fingerprints. It consists of several sheets of paper haphazardly attached together.

''We could have paid to have the petition flattened, but we felt its wrinkled appearance told its own story,'' said the exhibit's curator, Emily Soapes.