 Born on March 26, 1936, to a well-known family in Cebu, the Cuenco family, "Tony" was the son of former Gov.Manuel Cuenco and Milagros Veloso-Cuenco, the grandnephew of former Rep. Miguel Cuenco (5th district), and the grandson of the former Senate President, Mariano Jesús Cuenco.He was married to former congresswoman (2nd district), Nancy Roa-Cuenco with four children; Cebu City Councilor James Anthony Cuenco, Cebu City Councilor Ronald Cuenco, Antonio Cuenco, Jr., and Cynthia Cuenco-Dizon.