Eulalio Ríos had the following podium finishes at major championships: 1st in the 1955 Pan American Games 200 metre butterfly, 3rd in the 1955 Pan American Games 4×100 metre medley (with Clemente Mejía, Walter Ocampo, and Otilio Olguín), 3rd in the 1959 Pan American Games 200 metre butterfly, 3rd in the 1959 Pan American Games 4×100 metre medley (with Alejandro Gaxiola, Jorge Escalante, and the non-Olympian Roberto Marmolejo).
Died circa 1980.
|1956 Summer||21||Melbourne||Swimming||Men's 200 metres Butterfly||Mexico||MEX||6|
|1960 Summer||25||Roma||Swimming||Men's 200 metres Butterfly||Mexico||MEX||5 h1 r2/3|
|1956 Summer||21||Melbourne||Swimming||Mexico||Round One||Heat Two||3||QU||2:28.1|
|1960 Summer||25||Roma||Swimming||Mexico||Semi-Finals||Heat One||5||2:24.2|
|1960 Summer||25||Roma||Swimming||Mexico||Round One||Heat Two||3||QU||2:22.7|