The results of studies of yeast cytoplasmically-inherited determinants [psi] and [URE3] are summarized. The existence of tandem amino acid repeats in N-terminal regions of yeast Sup35p protein and in prions of higher eukaryotes is shown. The prion-like properties of yeast Sup35p and Ure2p proteins and a role of tandem amino acid repeats localized in N-terminal region of Sup35p protein in inheritance of [psi] determinants is discussed. The suggestion is made that the [psi+] status of yeast cell depends on the specific conformation of the N-terminal domain of Sup35p and that this protein can induce the specific conformational state of its N-terminal domain on newly synthesized Sup35p molecules via protein-protein interaction, thus representing a molecular basis of inheritance of [psi+] determinant. Other proteins containing amino acid repeats of similar type are considered and the suggestion is made that some of these proteins may show prion-like behavior.