One of the robes donated Monday comes from the family of the late writer Stetson Kennedy, who died in August some six decades after he infiltrated the KKK and exposed its secrets.
The second robe belonged to Phineas Miller Nathaniel Wilds, a chaplain in the Klan. It was donated by his great-great-grandson Richard Rousseau.
The $500 million museum is scheduled to open in 2015. Curators are planning exhibits spanning the journey of slaves from Africa, the Civil War, the civil rights movement and accomplishments in music, sports and culture.
Congress has pledged to provide about half of the cost.