The problem of 'vibronic' hyperfine coupling parameters in spin-coupled states of the dimeric mixed-valence clusters is considered in the framework of the adiabatic approach. The employed generalised vibronic model involves the interaction of the 'extra' electron with the local ('breathing' modes) and molecular (intermetallic) vibrations. The first type of vibrations produces a localisation effect while the second one promotes delocalisation. The explicit expressions for the hyperfine parameters in terms of the double exchange and two vibronic parameters are given, and the conditions are found under which the effect of partial delocalisation can manifest itself in the hyperfine structure of EPR for different spin states of the system. (C) 2000 Elsevier Science B.V.