Christopher Dow Marshall, 16, the son of Secretary of Labor and Mrs. Ray Marshall, died of cancer Wednesday at the National Institutes of Health in Bethesda.

A spokesman for the Cabinet officer said the youth was taken to the NIH hospital last week. His parents were with him when he died.

Doctors discovered cancer in Christopher's left arm at the end of 1977, and the arm was amputated in January 1978. But the disease spread to other parts of his body and he had been going to NIH for treatment since then.

Christopher was born in Baton Rouge, La. The family moved to Austin, Tex., while he was an infant. He was attending school there when his father was named to President Carter's cabinet in 1977.

The youth enrolled at Woodson High School in Fairfax, and would have started his senior year this fall. An outstanding student, he had been active in sports, particulary track.

In addition to his parents, he is survived by three sisters, Jill, Susan and Sarah, and a brother, John, all of the home at Mantua in Fairfax County.

The family suggests that expressions of sympathy be in the form of contributions to the Northern Virginia chapter of the American Cancer Society or the Capital Children's Museum of the District of Columbia. CAPTION: Picture, CHRISTOPHER D. MARSHALL