Are chronic fatigue syndrome and fibromyalgia autoimmune both diseases?

No: These are not autoimmune diseases. Many doctors think chronic fatigue and fibromyalgia are a neurologic response to stress, accidents, or illness which causes low energy and increased pain signalling. The exact cause is unknown but may be multifactorial, as a result of genes, environmental exposures and other factors.

Autoimmune disease: Neither disease is of the autoimmune variety. They tend to be diagnosed based on specific findings and very general symptoms.