"Each of the defendants has been charged by criminal complaint with knowingly and wilfully making false statements to the FBI in a matter involving international and domestic terrorism," the justice department said.
In supporting documents filed with the court, federal investigators said a laptop computer that contained an image of nine pages of handwritten notes was found during a September 11 search of Zazi's rental car in New York.
The notes included formulas and instructions on how to build explosives, detonators and other "components of a fusing system", the documents said.
Zazi allegedly was asked about the notes during FBI interviews last week and said he knew nothing about them.
The FBI's court filings also said Zazi admitted to FBI agents that he received weapons and explosives training at an al-Qaeda training facility in Pakistan in 2008.
A senior US intelligence official told the Associated Press news agency that Zazi played a crucial role in an intended terrorist attack but that it was not immediately clear what the targets were.
Art Folsom, Zazi's attorney, dismissed the official's remark, calling it "rumour".
Zazi has repeatedly denied any connection to al-Qaeda or to a purported terrorist plot.
The Zazis were scheduled to appear in federal court in Denver on Monday, while Afzali was to appear in the eastern district of New York.
If convicted each would face eight years in prison.