A complete overview of all possible periodic structures with characteristic H-bonding patterns is provided for oligomers composed of γ-amino acids (γ-peptides) and their vinylogues by a systematic conformational search on hexamer model compounds employing ab initio MO theory at various levels of approximation (HF/6-31G*, DFT/B3LYP/6-31G*, SCRF/HF/6-31G*, PCM//HF/6-31G*). A wide variety of structures with definite backbone conformations and H-bonds formed in forward and backward directions along the sequence was found in this class of foldamers. All formally conceivable H-bonded pseudocycles between 7- and 24-membered rings are predicted in the periodic hexamer structures, which are mostly helices. The backbone elongation in comparison to α- and β-peptides allows several possibilities to realize identical H-bonding patterns. In good agreement with experimental data, helical structures with 14- and 9-membered pseudocycles are most stable. It is shown that the introduction of an (E)-double bond into the backbone of the γ-amino acid constituents, which leads to vinylogous γ-amino acids, supports the folding into helices with larger H-bonded pseudocycles in the resulting vinylogous γ-peptides. Due to the considerable potential for secondary-structure formation, γ-peptides and their vinylogues might be useful tools in peptide and protein design and even in material sciences.