One was found a postal facility in New Castle, while another was found at a facility in Wilmington.
Law enforcement sources tell ABC News at least one of the packages is similar to crude pipe bombs sent to former President Barack Obama, Hillary Clinton, and CNN.
Action News has obtained a photo of one of the packages. The return address is the same as others that were sent around the country.
PHOTO: This is the pic of the suspected pipe bomb addressed to Joe Biden. The sender is the same as the others sent around the country. Supervisor who saw the package says the object inside seemed to be “shaped like a flashlight”. She immediately told employees to evacuate @6abc pic.twitter.com/ylXR4cQqIN— Jeannette Reyes (@6abcJeannette) October 25, 2018
It all began around 6 a.m. when the New Castle facility, on the 100 block of Quigley Boulevard, was evacuated and all mail trucks were moved to other facilities.
County police told Action News the FBI took over the investigation at the post office.
Then, just before 8 a.m., police responded to the postal facility in the 1500 block of Lancaster Avenue in Wilmington.
A supervisor says she saw that an object inside seemed to be "shaped like a flashlight" and told employees to evacuate.
Also Thursday, a suspicious package was discovered addressed to actor Robert DeNiro in New York City.
At least 10 suspicious packages were sent to prominent public figures this week.
Officials said all the packages were similar: manila envelopes with bubble-wrap interior bearing six stamps and the return address of Rep. Debbie Wasserman Schultz. She is the former chairwoman of the Democratic National Committee who was accused by Clinton rivals of secretly helping the party's eventual presidential nominee.
There was no indication Shultz was involved.
Authorities are calling these devices acts of terror, and they believe they are all connected.