The decomposition of Al₈₄Dy₆Ni₁₀ and Al₈₄Dy₈Ni₆Co₂ glasses prepared by melt spinning was investigated by means of X-ray diffraction (XRD), electrical resistivity (ER), calorimetric and microhardness measurements during isothermal, isochronal and continuous heating. Irreversible and reversible relaxation phenomena as well as glass transition occur before a primary crystallisation reaction in the ternary and a eutectic-type reaction in the quaternary alloy followed by the precipitation and transformation of intermetallic phases. Short- (SRO) and medium-range order (MRO) changes are responsible for pre-peaks in the structure factor observable even at room temperature. Glass transition (GT) is accompanied by resistivity drops. The first crystallisation products have a very fine morphology which raises the hardness of the alloys.