Bose-Einstein correlations are studied in semileptonic (WW-->qq ̄lν) and fully hadronic (WW-->qq ̄qq ̄) W-pair decays with the ALEPH detector at LEP at centre-of-mass energies of 172, 183 and 189 GeV. They are compared with those made at the Z peak after correction for the different flavour compositions. A Monte Carlo model of Bose-Einstein correlations based on the JETSET hadronization scheme was tuned to the Z data and reproduces the correlations in the WW-->qq ̄lν events. The same Monte Carlo reproduces the correlations in the WW-->qq ̄qq ̄ channel assuming independent fragmentation of the two W's. A variant of this model with Bose-Einstein correlations between decay products of different W's is disfavoured.