As he rose through the ranks he took part in the American Indian Wars, served in Puerto Rico during the Spanish–American War. He was with the 11th Infantry in 1901 when it was ordered to the Philippines during the Philippine–American War, and he served at Carigara on the island of Leyte. In 1902, he took part in combat against Filipino insurgents on Leyte and Samar, and in one engagement he was wounded by a bolo. During the Pancho Villa Expedition, Alexander served on the Texas–Mexico.