Fe and Fe/Cu multilayered nanowires with layer thicknesses in the 10nm range were successfully synthesized within the voids of nanoporous polycarbonate membranes and characterized by transmission electron microscopy. Magnetization measurements show that the shape anisotropy of individual Fe wires dominates the magnetic properties. Fe(8nm)/Cu(10nm) multilayered nanowires show CPP-GMR ratios as large as 12% at low temperature. The variations of the CPP-GMR as a function of the Cu layer thickness are consistent with the Valet-Fert model. Our data yield a value of about 0.3 for the bulk spin asymmetry coefficient beta.