By using the method to define a local structural motif of proteins by the Delaunay tessellation proposed by Wako and Yamato (Protein Eng. 11, 981-990 (1998)), we analyzed environment-dependent and position-specific frequencies of amino-acid occurrences in α-helices. In that method the three-dimensional structure of a protein molecule is uniquely divided into non-overlapping Delaunay tetrahedrons, each vertex of which is occupied by one of the comprising residues. A code is then assigned to each tetrahedron so as to characterize the local structure containing it. The tetrahedrons located in the interior of the α-helices are assigned 36 kinds of codes. The differences in the codes reflect the existence and absence of four residues surrounding the relevant region of the α-helix. In other words, the environment of the α-helix can be differentiated by these codes. Accordingly, we analyzed the frequencies of amino acid occurrences on each vertex of the tetrahedrons for each of these codes. Such data provide information about possible amino acid substitutions specific to a vertex position (i.e., a position in the α-helix) for a given code (i.e., environment around the α-helix). Furthermore, the principal component analysis was carried out to reveal general features of the amino acid occurrences in the α-helices. In relation to these results, such frequencies at the N- and C-terminals of the α-helix are also discussed.