The temperature dependence of the resistivity of three sputtered Fe/Cr superlattices was analyzed. Two are antiferromagnetic and one is ferromagnetic. Also, a series of Fe/Cr superlattices was characterized as a function of Cr thickness by means of resistivity, Kerr-rotation, and x-ray-diffraction measurements. Magnetoresistance measurements for films with 32-angstrom Fe layers confirm the presence of three oscillations with peaks at approximately 11, 27, and 42 angstrom Cr. The Kerr-rotation measurements for fixed Fe thicknesses of 15, 25, 32 and 40 angstrom indicate that the first antiferromagnetic region is always between approximately 6 and 17 angstrom Cr thickness. The low-angle x-ray results show that the structure is not ideal, based on comparison to dynamical simulation or to the quality of similarly prepared Fe/Mo superlattices. The magnetoresistivity of the antiferromagnetic films decays from its maximum value at low temperature with a T2 behavior below approximately 100 K, while a ferromagnetic film could be similarly approximated by a T3/2 behavior. These power laws are a consequence of the thermal excitation of magnons in these anisotropic antiferromagnetic and ferromagnetic superlattices, respectively. The resistivities due to sd-interband scattering rho-sd are approximated by a T2 behavior and roughly a T3 behavior, respectively. This indicates that for the antiferromagnetic films the dominant contributions to rho-sd come from processes mediated by magnons as well as phonons.