We have studied the phase and structure evolution of the Ti33Cu67 amorphous alloy subjected to electrical pulses of high current density. By varying the pulse parameters, different stages of crystallization could be observed in the samples. Partial polymorphic nanocrystallization resulting in the formation of 5- to 8-nm crystallites of the TiCu2 intermetallic in the residual amorphous matrix occurred when the maximum current density reached 9.7·108 A m-2 and the pulse duration was 140 μs, though the calculated temperature increase due to Joule heating was not enough to reach the crystallization temperature of the alloy. Samples subjected to higher current densities and higher values of the evolved Joule heat per unit mass fully crystallized and contained the Ti2Cu3 and TiCu3 phases. A common feature of the crystallized ribbons was their non-uniform microstructure with regions that experienced local melting and rapid solidification.PACS: 81; 81.05.Bx; 81.05.Kf.