The timing of alpha losses, with respect to the various phases of a disruption, and the impact location of the losses are characterized during high fusion power operation of TFTR with deuterium and tritium fuels. Characterization of alpha losses is important for the design of future fusion devices such as ITER. In addition, characterization of the alpha losses with respect to the disruption evolution helps in the understanding of the dynamics of the disruption process and related MHD events such as sawtooth crashes. Disruptions are characterized as having several standard phases, applicable to most disruptions in all tokamaks: precursor, thermal quench(es) and current quench. Most of the losses are observed to occur during the thermal quench phase(s). In high beta disruptions, alpha losses start abruptly during the growth of MHD precursors, just before the onset of the thermal quench. The initial burst of losses, lasting as little as 100 mu s, can release a significant fraction (one third) of the total disruption induced losses during the thermal quench. An inventory of alpha particles suggests that the alpha loss distribution during disruptions might be quite different from that expected during non-disruptive discharges. There are no obvious differences between fast fusion product losses during deuterium-deuterium (DD) and deuterium-tritium (DT) disruptions, aside from the large alpha loss component in DT discharges