We studied the electrical and optical properties of X2YZ (X = Co, Fe; Y = Cr, Mn, Ti; Z = Ga, Al, Si) Heusler alloys. We showed that the electrical and optical properties of Co2TiAl and Fe2TiAl are typical of metals. An abnormal behavior of the resistivity and the optical properties in the IR range of the other alloys was observed, i.e., the resistivity exhibits a semiconductor-like behavior and the optical conductivity has no contribution from the intraband absorption of the conduction electrons. The experimental data analysis, based on existing band calculations, allowed us to conclude that the anomalous behavior of their properties is determined by electronic states near to and at the Fermi level. The electronic states in the subband with spin up give the main contribution to the interband transitions in the IR range, but they practically do not contribute to the static conductivity (resistivity). There are almost no charge carries in the other electronic subband (with spin down), and hence, the interband transitions occur only at the energies above the semiconductor gap values.