Friends and neighbors identified the family as 42-year-old Matthew Edwards, his wife 41-year-old Julie Burton Edwards, and their children, 6-year-old Jacob, 4-year-old Brinley, and 3-year-old Paxton.
The five died of apparent gunshot wounds.
Police were called around 8 p.m. to the home on the 2700 block of Ferris Road. A neighbor said he believed a teenage boy found the family of five.
The neighbor told ABC7's sister station WPVI-TV just 24 hours before that the father had been emotional about work and marital issues.
The neighbor consoled him and said, "Just worry about your kids."
Autopsies will be performed to determine the exact cause of death.
Despite the large police presence at the scene, Delaware State Police said there was no concern for public safety.
If anyone has information about this incident, they are asked to contact Detective D. Grassi of the Delaware State Police Homicide Unit at 302-365-8441.