He played several times in Argentine championships (Torneo Mayor). In 1931, he took 12th place (Jacobo Bolbochán won); took 4th in 1932 (Isaias Pleci won); took 2nd, behind Luis Piazzini, in 1933; tied for 5-7th in 1934 (Roberto Grau won); took 5th in 1935 (Jacobo Bolbochán won); took 11th in 1936 (Carlos Guimard won); took 10th in 1937 (Jacobo Bolbochán won); tied for 7-8th in 1938 (Grau won).
Iliesco finished 1st in Argentine championship in 1939, but he could not win the title as a foreigner (Romanian citizen). In 1940, he tied for 7-9th (Guimard won); took 6th in 1941 (Markas Luckis won); tied for 3rd-4th in 1942 (Herman Pilnik won); took 2nd, behind Gideon Stahlberg, in 1943; shared 6th in 1944 (Hector Rossetto won). Iliesco (then Argentine citizen) lost a match for the title to Rossetto (0.5 : 4.5) at Nueve de Julio 1944.
He took 3rd in ARG-ch 1945 (Pilnik won); took 9th in 1946 (Julio Bolbochán won); took 4th in 1947 (Rossetto won); tied for 10-11th in 1948 (Julio Bolbochán won); shared 17th in 1949 (Miguel Najdorf won); took 11th in 1950 (Carlos Maderna won); tied for 18-19th in 1953 (Oscar Panno won).
Iliesco played also many times in international tournaments in Mar del Plata. He tied for 12-13th in 1934 (Aaron Schvartzman won); took 6th in 1936 (Pléci won); took 15th in 1941 (Stahlberg won); tied for 14-15th in 1942 (Najdorf won); shared 10th in 1943 (Najdorf won); tied for 13-14th in 1944 (Pilnik and Najdorf won); took 11th in 1945 (Najdorf won); tied for 12-15th in 1946 (Najdorf won), and took 18th in 1947 (Najdorf won); took 9th in 1949 (Rossetto won).
- Brillantes partidas argentinas, Guillermo Puiggros, page 146
- "List of players who remained in Argentina in 1939 (notes in Spanish)". Archived from the original on 2009-10-21.
- "Major Tournaments and Argentine Chess Championships (notes in Spanish)". Archived from the original on 2009-10-25.