Excavators found, in the center of the structure, the statue of Emperor Tiberius which helped with the accurate dating, on the1st century A.D.
The Agora was a central public structure in ancient Greek city-states. The literal meaning of the word is a "gathering place" or "assembly". It was usually the center of athletic, artistic, spiritual and political life of the city.
Sanctuaries, that became centers for competition whether athletic, musical, dramatic, or festivals and celebrations in honour of a god/goddess, usually have such structures. Gymnasium, where sprinting and longer distance racing could be practiced alongside, discus or javelin throwing and long jumping, could be used also as a place of study philosophical discussion and other mental activities. Moreover, in antiquity, a Gymnasium was highly standardized both in architecture and function and it played a key role in young male’s physical and general education.
The structure of Gymnasium became a common feature across the Greek world and was adopted by the later Romans, evolving into the huge multi-purpose complex, the Roman baths. Usually besides the Gymnasium was a Palaistra or a Stadium. All these features were located outside but adjacent to the shrine.
Unfortunately, the current bad preservation of Eleusina’s Gymnasium or Agora makes more difficult the acquisition of further information.