Field-dependent transverse permeability characterization of amorphous thin films with nominal composition Fe73.5Cu1Nb3Si13.5B9 was performed for frequencies in the range of 100 kHz–1.8 GHz. Dynamic and static magnetic properties were investigated in films with thickness in the range from 21 to 5000 nm. Samples with thicknesses below 85 nm exhibit a well-defined in-plane uniaxial anisotropy and uniform ferromagnetic resonance modes. Samples thicker than 85 nm were found to be magnetically isotropic in the plane, with complex magnetic dynamics depicted by several ferromagnetic resonance modes detected at relatively low fields. The results are discussed in terms of the stress contribution to the magnetic anisotropy of the samples.