Nickel and zirkonium self-diffusion in the amorphous and the supercooled liquid state of the bulk metallic glass Zr46.75Ti8.25Cu7.5Ni10Be27.5 has been investigated using the radiotracer method. Encompassing four orders of magnitude in the diffusivity self-diffusion of 63Ni cannot be fitted to a single Arrhenius function. The deviation from an Arrhenius function is attributed to differences between the supercooled liquid and glassy state. This explanation is supported by recent diffusion studies reported by other authors. Self-diffusion of the major component studied with the isotope 95Zr is much slower compared to the above-mentioned measurements. We also performed high pressure experiments in the supercooled liquid state from which activation volumes for 63Ni diffusion of about one mean atomic volume were deduced. This suggests that diffusion in the supercooled liquid state proceeds by a hopping process involving vacancy-like defects.