The group says the city is discriminating against them because they say that they're allergic to the wireless Internet signal.
Arthur Firstenberg says he is highly sensitive to certain types of electric fields, including wireless Internet and cell phones.
"I get chest pain and it doesn't go away right away," he said.
Firstenberg and dozens of other electro-sensitive people in Santa Fe claim that putting up Wi-Fi in public places is a violation of the Americans with Disabilities Act.
City Councilor Ron Trujillo says the areas are already saturated with wireless Internet.
"It's not 1692, it's 2008. Santa Fe needs to embrace this technology, it's not going away," Trujillo said.