An Al₂₅La₅₀Ni₂₅ and newly discovered Al₃₈Dy₅₀Ni₁₂, Al₃₈Dy₅₀Co₁₂ and Al₄₁Dy₄₇Ni₆Co₆ glasses prepared by melt-spinning were studied by means of electrical resistance (ER) and calorimetric measurements at constant and at linearly increasing temperatures as well as by X-ray diffraction (XRD) and microhardness studies after different heat treatments. Changes in short-range order during relaxation lead to prepeaks in XRD spectra, ER and hardness increases. The glass transitions are accompanied by endothermal heat effects and ER drops. In Al₂₅La₅₀Ni₂₅, crystallisation sets in above 240 °C via the formation of metastable LaNi and AlLa₃ phases which may transform into La(Ni, Al). The Al₃₈Dy₅₀Ni₁₂ glass crystallises only above 400 °C; fine precipitates of Dy₃Ni and probably DyAl appear before a Dy(Ni, Al) phase forms. The Co-containing materials possess still increased stability but are very brittle.