A systematic study of the electrical resistivity (\ensuremath{\rho}) has been carried out between 10 and 600 K on substitutionally disordered \ensuremath{\gamma}-${\mathrm{Fe}}_{80\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ni}}_{\mathit{x}}$${\mathrm{Cr}}_{20}$ (14\ensuremath{\le}x\ensuremath{\le}30) austenitic stainless steel alloys in different magnetic states. We observe in each alloy, irrespective of its low-temperature magnetic state, a strong deviation from linearity (DFL) of \ensuremath{\rho} which is an indication of resistivity saturation at high temperatures. The temperature coefficient of resistivity (TCR=${\mathrm{\ensuremath{\rho}}}^{\mathrm{\ensuremath{-}}1}$d\ensuremath{\rho}/dT) vs \ensuremath{\rho} curves for all the alloys merge in the temperature range of 100 to 600 K. This behavior indicates that both thermal and compositional disorders are equally important in determining the resistivity saturation. We have examined several models and find that the parallel-resistor and the ion-displacement models are the most appropriate ones in explaining this DFL of \ensuremath{\rho} at high temperatures. At low temperatures, in the long-range ferromagnetic and antiferromagnetic as well as in the mixed-phase regimes, the contribution to resistivity from the electron-magnon scattering (\ensuremath{\sim} ${\mathit{T}}^{2}$) dominates. In the spin-glass regime there is an additional ${\mathit{T}}^{3}$ term arising from the electron-phonon scattering in the presence of an s-d interaction. \textcopyright{} 1996 The American Physical Society.