It is shown that anomalously large and anomalously small values of the constant A in the thermionic current formula for metals can be explained by the usual statistical equilibrium theory provided proper account is taken of the fact that free electrons may be shared by two competing overlapping energy bands. When this theory is developed there arises a comparatively large temperature variation of the statistical parameter ζ which occurs in the Fermi function, and when the exact formula is forced into the empirical form with a constant work function, the temperature factor appears as a multiplying factor of the current constant, this factor being greater or less than unity depending upon the nature of the overlapping bands. In particular the observed values of the constant A for nickel and for hafnium are well explained.