There are typically two parts to the process; first, the exchange of unused stamps for new ones of equivalent value. This normally occurs at post offices, with patrons bringing in their old stamps. The second part is the handling of mail with stamps already on it. Uncancelled letters, such as those dropped in mailbox, will get a grace period, ending at roughly the same time as the exchange of old stamps. Cancelled letters already in the mailstream may be accepted for a longer period, since remote post offices may not yet have exchanged their stamps, and sometimes there may be delays within the postal system itself.
United States postage stamps have only been demonetized twice. The first time was in 1851, when the 5-cent and 10-cent stamps of the 1847 issue were declared invalid as of July 1 by the Act of March 3, 1851 reducing the normal letter rate from five to three cents. A few dozen covers are known that carry 1847 stamps after the demonetization date; as stamp usage was then still optional (it would not be made mandatory until 1855), the demonetization seems to have had relatively little impact.
The second, more serious, demonetization was prompted by the outbreak of the American Civil War in 1861. Southern post offices held substantial U.S. assets in the form of their stamp stocks, and the Confederates could theoretically have brought in some income by selling those stamps to private individuals in the North. Although in April 1861 John H. Reagan, postmaster of the CSA, ordered the offices in his charge to return their stamps to Washington D.C., few seem to have done so, and by June 1861 U.S. postmaster-general Montgomery Blair ordered the severance of postal ties and the production of new stamps. In August the stamps of the U.S. 1861 issue began to be distributed throughout the Union, along with orders that postmasters should offer to exchange old stamps for new for a period of six days after giving "public notice through the newspapers and otherwise". After the six-day period was over, that post office was not to recognize the old stamps as paying postage. In addition, postmasters were to accept letters with old stamps from other post offices until set dates, ranging from September 10 in the East, to November 1 from letters arriving from the Far West. (Later the periods were extended for an additional two months.) The process stretched over some months; the large cities in the East were exchanging stamps in the third week of August, while some small remote offices did not start until November. General confusion, combined with exhaustion of the new stamps at some post offices, led to some instances of the old stamps still being accepted on letters after demonetization, although surviving covers are rare.
The U.S. stamps of 1861, and all issued since then, continue to be valid on mail.
In the United Kingdom, earlier issues have been demonetized on several occasions. The first when stamps issued during the reigns of Queen Victoria and King Edward VII (issued 1840 to 1911) were declared no longer valid for postage. The second, early in 1970, when the stamps issued during the reigns of King George V, King Edward VIII and King George VI (issued 1911 to 1952) ceased to be valid and the third some months after the introduction in 1971 of decimal currency, when all stamps with pre-decimalization values were demonetized. Queen Elizabeth II £1 value stamps issued prior to 1971 are identifiable by design but remain valid for postage.
These stamps on cover, two from each of four reigns, with face value of five pence, the minimum first class letter rate in 1969, were all valid for postage and the cover was delivered next day. Six were demonetised in 1970 and the remaining two in 1971.
The country of Poland has a very recent example of demonetization involving the stamp issues of 1990 to 1994. During this period of time, the face values of stamps due to hyper inflation gradually changed the face values to thousands of zloty. Commemorative stamp issues from 1995 to 1997 are also demonetized now as are certain selected issues as announced by the Polish Post Office.
When a newer stamp issue is demonetized a date is announced, however, if a postal patron in a small town has not been notified of the demonetization or a postal patron does not visit their local Post Office often, then Polish Post Office will accept their obsolete stamps for letter franking well after the demonetization date.