Behaviour of thermal spin waves (SW) localized on an array of Fe(20 nm)/Au(1 nm)/Fe(20 nm) stripes has been studied. Measurements of spectra of SW resonances on 1.0 and 1.5 mum wide stripes carried out by means of Brillouin light scattering (BLS) technique have revealed strong positive exchange coupling (A(12) = 0.8erg/cm(2)) between the two ferromagnetic layers. An improved analytical theoretical technique, simple but efficient, has been developed. It allows taking into account interlayer exchange interaction, affecting the relative position of the two dispersion branches, surface optic (SO) and surface acoustic (SA), as well as dipolar interactions governing the shape of each dispersion branch and "effective dipolar- pinning conditions" at the stripe edges for relatively thick films. To this end, the terms responsible for dipolar "cross-talk" between non-identical components in two layers, have been added. Theoretical predictions are in good agreement with experimental results. (C) 2004 Elsevier B.V. All rights reserved.