In the other, four electrical fuses for ballistic missile warheads were mistakenly sent to Taiwan instead of helicopter batteries that had been ordered.
Gates said an internal investigation found a common theme in the B-52 and Taiwan incidents: "a decline in the Air Force's nuclear mission focus and performance".
He said that his decision to remove Wynne and Moseley was based on the findings of an investigation of the Taiwan debacle by Admiral Kirkland Donald, which found a "lack of a critical self-assessment culture" in the air force, making it unlikely that weaknesses in the way critical materials such as nuclear weapons are handled could be corrected.
He also said that Donald found a "lack of effective air force leadership oversight" of its nuclear mission.
Moseley said "as the air force's senior uniformed leader, I take full responsibility for events which have hurt the air force's reputation or raised a question of every airman's commitment to our core values".
Wynne said he "read with regret" the findings of the report into the Taiwan debacle.
Gates said he would make recommendations to the US president shortly on a new air force chief of staff and civilian secretary.