Structural transitions on heating a ZrCu martensite prepared by induction melting and subsequent rapid cooling have been investigated by means of differential scanning calorimetry (DSC), electrical resistivity measurements, X-ray diffractometry (XRD) and transmission electron microscopy (TEM). The ZrCu martensite firstly transforms to the ZrCu compound with the B2 structure at around 300degreesC. Depending upon the annealing temperature, there are two routes for the ZrCu compound to reach equilibrium. By annealing at T greater than or equal to 425degreesC, the equilibrium state, i.e. a eutectoid mixture of Zr7Cu10 and Zr2Cu, is attained directly because the required chemical segregation for the equilibrium phases can be satisfied; alternatively, by annealing at 300degreesC < T < 425degreesC, the equilibrium state is reached via another metastable state, an amorphous phase. This is, however, present only locally and contains significant levels of oxygen. A qualitative explanation of the observed structural transitions is given in terms of thermodynamic and kinetic considerations.