  Within the Kubo-Greenwood formalism we use the fully relativistic,
spin-polarized, screened Korringa-Kohn-Rostoker method together with the
coherent-potential approximation for layered systems to calculate the
resistivity for the permalloy series Ni$_{c}$Fe$_{1-c}$. We are able to
reproduce the variation of the resistivity across the entire series; notably
the discontinuous behavior in the vicinity of the structural phase transition
from bcc to fcc. The absolute values for the resistivity are within a factor of
two of the experimental data. Also the giant magnetoresistance of a series of
permalloy-based spin-valve structures is estimated; we are able to reproduce
the trends and values observed on prototypical spin-valve structures.
