In 1961, Cuéllar won in Caracas (zonal). In 1962, he placed 22nd at the Stockholm Interzonal, defeating both Efim Geller and Viktor Korchnoi in individual games. In 1966, he took 7th in Havana (Eleazar Jiménez won). In 1967, he tied for 19-20th in Sousse (interzonal; Bent Larsen won). In 1969, he tied for 1st with Boris De Greiff in Bogotá. In 1970, he took 7th in Bogotá (Henrique Mecking won). In 1970, he took 14th in Caracas (Lubomir Kavalek won). In 1972, he won the Zonal tournament in Bogotá, and qualified for the 1973 Leningrad Interzonal, but finished there in last place (Anatoly Karpov and Viktor Korchnoi won). In 1980, he tied for 4-5th in Bogotá (Joaquin Gutierrez won).