The statistical properties of the Barkhausen noise (BN) in thin amorphous films are studied as a function of both the nominal composition and the thickness. BN was observed in single films with nominal compositions Fe73.5Cu1Nb3Si22.5-xBx (with x = 4 and 9) in the thickness range 20 nm-5 mu m. The distributions of Barkhausen jump sizes and duration times were obtained and fitted to power laws with critical exponents tau = 1.25 +/- 0.05 and alpha = 1.60 +/- 0.05, respectively. (c) 2006 Elsevier B.V. All rights reserved.