The permeability of the magnetic material in a thin-film magnetic head is an important, but hard to characterize, parameter since the magnetic permeability depends on the head domain structure, the drive frequency, and the shape and size of the head. We have measured the high-frequency permeability from 1 MHz to 300 MHz, hysteresis loops, and domain structure of unlaminated and multilayer magnetic thin-films as a function of stripe width for arrays of long narrow stripes. Monolithic permalloy films and permalloy films laminated with SiO2 have been photolithographically patterned and ion-milled to create 3 to 1000 μm wide rectangles, 1 cm long, with the hard axis oriented along the long axis of the rectangles. The high-frequency permeability of each array of a given width is measured by the signal detected by a nonresonant butterfly-coil pickup loop when the film is driven by a uniform radio-frequency magnetic field generated by a strip-line waveguide. The changes in domain pattern as the film structure and stripe width are varied are observed with a Kerr-effect imaging microscope. In unlaminated films, which exhibit standard closure domains, a reduction in high-frequency permeability is observed in agreement with simple models when the closure domains become a significant fraction of the film area. In laminated films with thick magnetic layers, the transition from the laminated domain state to closure domains as the stripe width is decreased occurs where expected from straightforward energy arguments. However, for magnetic layers less than 1 μm thick, where a transition from the easy-axis laminated domain state to a uniform hard-axis state is expected as the stripe width is reduced, the films first change from the easy-axis state to a complicated, low-Kerr-contrast domain pattern before switching to the hard-axis state at much larger widths than predicted. While the laminated state and hard-axis permeabilities are frequency independent, the permeability of the intermediate state rolls off beginning at between 10 and 100 MHz. For still thinner magnetic layers (250 Å), the multilayer retains the high-permeability easy-axis laminated domain state to the narrowest width measured, 3 μm.