The Office of the Commissioner of Baseball announced that Atilano received a 50-game suspension after a second violation for a drug of abuse.
Duarte also received a 50-game ban after testing positive for an amphetamine.
The suspensions are effective immediately.
Atilano, who appeared in 16 Major League games for the Nationals in 2010, has pitched in only two games this season. His last appearance came on April 16 with Double-A Pensacola and he also made one start for Triple-A Louisville but has been on the disabled list for much of the year.
The 27-year-old was drafted by the Braves, who traded him to Washington for Daryle Ward in 2006. He was a 2005 South Atlantic League All-Star and went 6-7 with a 5.15 ERA in 16 outings with the Nationals in the 2010.
Duarte, 25, has bounced around in recent years but was 2-0 with a 2.12 ERA in 15 outings between Double-A Portland and Class A Advanced Salem this season. He was signed by the Rockies in 2007 and loaned to the Mexican League, selected by the Astros in the 2011 Rule 5 Draft and eventually signed with the Red Sox as a free agent in December 2011. This is his first season with Boston.
Major League Baseball has suspended 49 players this year for violations of the Minor League Drug Prevention and Treatment Program.