Rhesus factor incompatibility, commonly referred to as Rh incompatibility, is a condition that can occur during pregnancy when the blood types of a pregnant woman and her baby or fetus do not match. The difference in blood type, if not properly managed, can result in a notable health risk for the unborn child. Understanding Rh incompatibility, its possible consequences, and management, is imperative for expecting parents and soon-to-be couples, a report by the Cleveland Clinic said. Rhesus Factor The Rhesus (Rh) factor is an inherited protein found on the surface of red blood cells. A person who has no protein on his or her Red Blood Cells (RBC) is Rh negative.