There were two sets of Nuremberg Trials.
The first, and most well known, were the criminal trials of the leaders of Nazi Germany. They were organized by the International Military Tribunal (IMT). The judges and prosecutors were from the four wartime Allies: France, the USSR, the United Kingdom and the United States.
The second set of trials were the 12 follow-up trials (German: nachfolgende Prozesse). These trials were of groups of lower-ranking Nazis, like doctors, and officials of the German Foreign Office. Although the follow-up trials were held in the same courtroom as the IMT trials, they were run by the Americans alone.