Well-defined electron spin resonance (ESR) lines have been detected recently in several heavy fermion compounds, in which ferromagnetic correlations appear to be present. We first discuss the theory of ESR for the Kondo impurity system at temperatures T<<TK (Kondo temperature) , where the local spin ESR line has a width of order TK and is therefore unobservably broad. By contrast, in the Anderson lattice system in the Kondo regime the ESR linewidth is narrow, but gets broadened by spin lattice relaxation. We show that the spin lattice induced ESR linewidth is greatly reduced by an effective mass factor and by exchange narrowing induced by a ferromagnetic exchange interaction. This explains the observed ESR data.