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A model of the α-cluster radioactivity of even-even nuclei is presented. In this model, the collective motion in mass-asymmetry coordinate determines the probability to form a cluster in the surface region of the nucleus. The tunneling in the coordinate of the relative distance between the centers of mass of the cluster and the daughter nucleus determines the penetrability of the barrier of the nucleus-nucleus potential. The calculations was performed in the two-potential approach. The α-decay half-lives are calculated for various Ra, Th, U, and Pu isotopes. The fine-structure of alpha-decay, i.e. the relative yields of alpha-decay from the ground-state of the mother nucleus to the various yrast states of the daughter nucleus is demonstrated on the particular examples of 〖^230〗Ra, (^232)Th and (^240)Pu.