In the later manuscripts of Edmund Husserl one can find particular remarks on so called archaeology as a broadening of his methodology. In the first part of the paper the dynamics and possibilities of the phenomenological archaeology are described. In its second part the achievements of this archaeology are joined with the interpretational context of the relation between I and Alien-to-I as so called Core- Structure. Attention is paid to the formation and development of this structure with regard to the problematic of activity and affectivity, of I as “I-can.” These topics are then investigated in the context of Edmund Husserl’s Later Texts on Time Constitution (1929-1934).