Experimental measurements of the residual resistivity ρ(x) of the binary-alloy system Fe1−xCrx have shown anomalous concentration dependence which deviates significantly from Nordheim’s rule. In the low (x<10%) Cr concentration regime the resistivity has been found to increase linearly with x until ≈10% Cr where the resistivity reaches a plateau persisting to ≈20% Cr. In this paper we present ab initio calculations of ρ(x) which explain this anomalous behavior and which are based on the Korringa-Kohn-Rostoker method in conjunction with the Kubo-Greenwood formalism. Furthermore we are able to show that the effects of short-range ordering or clustering have little effect via our use of the nonlocal coherent-potential approximation. For the interpretation of the results we study the alloy electronic structure by calculating the Bloch spectral function particularly in the vicinity of the Fermi energy. From the analysis of our results we infer that a similar behavior of the resistivity should also be obtained for iron-rich Fe1−xVx alloys—an inference confirmed by further explicit resistivity calculations. Both of these alloy systems belong to the same branch of the famous Slater-Pauling plot, and we postulate that other alloy systems from this branch should show a similar behavior. Our calculations show that the appearance of the plateau in the resistivity can be attributed to the dominant contribution of minority-spin electrons to the conductivity which is nearly unaffected by the increase in Cr/V concentration x, and we remark that this minority-spin electron feature is also responsible for the simple linear variation in the average moment in the Slater-Pauling plot for these materials.