In 1980, Conz won her first attempt at the marathon in the Five College Marathon in South Hadley, Massachusetts. This was a qualifier for the marathon in London, England.
In August 1980, Conz ran her first international race and won second place at the Avon International Marathon for Women in London, England.[3] Conz wore bib number 184. Conz finished in 2:36:02,[3] and it was also the #2 time in the world that year. She returned the following year to win Avon, this time in Ottawa, beating her friend and future, winning the first ever women's Olympic gold medalist in the marathon, Joan Benoit.[4] She also won Freihofer's Run for Women that same year. In 1982, she won the Chicago Marathon with a personal best of 2:33:22.
Nancy was a great runner. She came onto the scene rather quickly, and climbed quickly as well. She was a real tenacious runner. She gave it everything she had. She beat me several times when we went head to head. She was tenacious and worked very hard.