The magnetic-field dependence of the magnetoresistance MR(H) has been measured in the CPP mode (current perpendicular to the plane) for multilayers containing three different types of magnetic layers: permalloy Py(80 Angstrom), Co(10 Angstrom), and Co(70 Angstrom). These data clarify the role of the electron mean free path in interpreting the MR(H) curves. A critical discussion is given of the view that denies the role of the electron mean free path for determining the MR(H) curves.