Transformations of the quasi-crystalline icosahedral phases formed in the melt-spun AlMn(Si) alloys Al90Mn10, Al86Mn14 and Al75Mn20Si5 have been studied at high temperatures (300-1000 K) by combined measurements of resistivity, differential scanning calorimetry and X-ray diffraction. In Al86Mn14 a direct crystallisation of both the icosahedral phase and the intergranular AlMn solid solution into o-Al6Mn is observed. It is preceded by a `relaxation' phenomenon, as seen by the DSC curve. The amplitude and temperature dependence of resistivity are well understood by taking into account the different phase contributions to resistivity during the transformation. The same analysis accounts for the measurements of the Al90Mn10 sample. The crystallisation of Al75Mn20Si5 into β-Al9Mn3Si is more complex and involves several intermediate crystalline phases, in particular the α-Al12Mn3Si. Finally, the better stability of the icosahedral phase in Al75Mn20Si5 (~700 K) compared with AlMn samples (~600 K) suggests possible structural and electronic differences between the two icosahedral phases