The magnetic behaviour of Fe/Cu multilayers produced by electron-beam evaporation has been investigated in the range 5 to 400 K and in magnetic fields up to 1 kOe using SQUID magnetometry. The multilayers exhibit an irreversible behaviour below a characteristic temperature . Low-field DC magnetic moment measurements on samples cooled in zero field revealed the usual signature of a spin-glass state. Time relaxation of the remanence and frequency-shift of the peak of the imaginary part of the AC magnetic moment were also observed. The irreversibility line was fitted to a de Almeida-Thouless line with a crossover critical exponent . We have interpreted these results as being due to the presence of some interdiffusion between Fe and Cu at the interfaces. The surprisingly high characteristic irreversibility temperatures indicate that diffused Fe atoms aggregate in clusters at the interfaces.