We describe the anomalies in the electronic properties of zero-gap semiconductors doped with transition elements (iron, chromium) that form deep resonance donor states, i.e., states degenerate with the continuum of the conduction band. We present an analysis of the numerous studies that shows that the distinctiveness of the properties of the materials being discussed, in particular, such a marked anomaly as increased electron mobility with increasing concentration of the dopant, is due to the correlated distribution of the charged donors in the crystal. The study of resonance states in semiconductors is a new field in solid-state physics, which at the same time is of practical interest, since it enables one, for example, to obtain materials with maximal electron mobilities.