"We have loved each other for a very long time and we share four incredible sons together," Gilbert said in a statement issued to People.com Tuesday. "On behalf of our family we ask to be allowed our privacy during this very difficult time."
The couple married in 1995 and are the parents of a 15-year-old son.
Gilbert, who is best known for her portrayal of Laura Ingalls Wilder on TV's "Little House on the Prairie," also has a 21-year-old son from her previous marriage to Bo Brinkman.
Boxleitner, famous for his shows "How the West Was Won," "Scarecrow and Mrs. King" and "Babylon 5," has two sons -- ages 30 and 25 -- from his marriage to actress Kathryn Holcomb.
Celebrity Couples of 2014 [PHOTOS]