Born on February 27, 1919, son of spouses Paulo Almendras and Elisea Mercado Durano of Danao, Cebu.
Finished his high school at the Cebu Provincial High (now called the Abellana National School) in 1938, took up aeronautical engineering at the Far Eastern University. Enlisted with the Philippine Air Force and when the USAFFE surrendered to the Japanese Imperial Army in 1941 went back to Cebu and became part of the corps of officers of Col. James Cushing. Alejandro was designated as commander at the young age of 23 of the 88thInfantry Regiment of the Cebu Area Command.
After the war, Alejandro went back to school and enrolled at the Mindanao Colleges in Davao City when he was asked to run for governor in 1951. He replaced Ricardo D. Miranda, the first elected governor after the war in 1948. Alejandro was governor of Davao from 1951 up to 1958. Succeeding him as governor of Davao was Cebuano lawyer Vicente Duterte who married Soledad Roa (they are the parents of Mayor Rodrigo Duterte). The couple (Duterte's) migrated to Davao in 1951. The wife of Ramon "Noy Amon" Durano named Beatriz was a Duterte and was a first cousin of Gov. Vicente Duterte. The sister of Noy Amon named Elisea married Paulo Almendras, who is the father of Alejandro.
Alejandro was awarded as the Outstanding Veteran in 1958 for his exploits during the war.
He was appointed by President Carlos P. Garcia as the first Secretary of the Department of General Services on May 8, 1959, months later he was drafted to be part of the senatorial slate of the Nacionalista Party of the incumbent president.
He was elected senator in the 1959 midterm elections held on November 10 of that year, clinching the last spot which was number 8. The first place was Ferdinand Marcos of the Liberal Party. The other Cebuano who won in that election was Mariano Jesus Cuenco (grandfather of Congressman Antonio V. Cuenco) a party mate of Alejandro of the Nacionalista Party.
In the senatorial elections of November 19, 1965, Ferdinand Marcos now a president defected to the Nacionalista Party, topping the list was Jovito Salonga of the Liberal Party, the second placed went to a Cebuano, Alejandro D. Almendras of the Nacionalista Party. The third place went to Genaro Magsaysay of the Nacionalista Party. Another Cebuano won in that election, that person was Sergio "Serging" V. Osmeña Jr. of the Liberal Party.
Alejandro was reelected in the 1971 senatorial elections. The senate was however physically padlocked by President Marcos when he declared Martial Law on September 21, 1972. Alejandro later became a Member of the Interim Batasang Pambansa representing Region XI or Southern Mindanao from June 12, 1978 up to June 5, 1984.
The grandfather of Alejandro was Juan Almendras who married Cecilia Gonzales. A sister of Alejandro, Cecilia Almendras de la Paz was appointed OIC governor of Davao del Norte replacing Atty. Jesus T. Albacite who assumed the position for 21 days. Cecilia was OIC governor until February 3, 1988 when the newly elected governor, Prospero S. Amatong, took his oath. Another brother, Priscillano was vice governor of Cebu during the term of Gov. Rene Espina.