Philatelists usually class the 1921-1927 issues of the East Africa and Uganda Protectorates and Kenya and Uganda under the KUT rubric, but the first issues spelling out all the names of the colonies came in 1935, in the form of common design commemoratives for the Silver Jubilee of King George V as well as a definitive series featuring a profile of the king and local scenes. The definitives included a dramatic departure form the usual engraved stamps of the period; the 10c and 1lb stamp were typographed and had a silhouette of a lion, with color combinations of black/yellow and black/red, respectively.
The same designs were reissued in 1938 with a profile of George VI. Wartime exigencies forced the use of surcharges on four South African stamps in 1941 and 1942, but after the war the usual common types (Peace Issue, Silver Wedding Issue, etc) resumed. A definitive series, with new designs, was issued in 1954 for Queen Elizabeth, and in 1958 a pair of commemoratives marked the 100th anniversary of the discovery of the Great Lakes of Africa by Burton and Speke.
A new definitive series in 1960 used simpler and more symbolic designs, and was followed in 1963 by three sets of commemoratives. At this point the East African Commo Services Organization took over, and issued commemoratives for the 1964 Olympic Games inscribed "UGANDA KENYA TANGANYIKA ZANZIBAR", even though they were never actually used in Zanzibar. Tanganyika having changed its name to Tanzania, subsequent stamps were inscribed "UGANDA KENYA TANZANIA", with the three names being listed in randomly varying orders.
These stamps were issued in parallel with stamps from each of the newly-independent nations. The postal administration continued to issue various commemoratives, at the rate of about 10-12 per year, until early in 1976.