Evidences of both sluggish eutectoid and active eutectoid (not suppressible under rapid cooling) transformations have been found for the first time in a single hyper-eutectoid Ti-Cu alloy. Both of these types of eutectoid reactions have been investigated in detail, at different length scales, by coupling scanning electron microscopy (SEM), transmission electron microscopy (TEM) and atom probe tomography (APT). The unique three phase crystallographic relationship between the parent β(bcc) and the two product phases, α (hcp) and Ti₂Cu, has been established. The extent of partitioning of the solute (Cu) between the two product phases has been determined by APT and is rationalised in terms of thermo-dynamic considerations. Based on the observed lattice site correspondence and the extent of solute partitioning, a possible mechanism of active eutectoid transformation is proposed.