The presence in graphyne sheets of a variable amount of sp2 and sp1 carbon atoms suggests a high ability of these nanostructures for saturation. E.g., covalent binding of chlorine atoms would lead to sp3- and new sp2 hybridized carbon atoms, and the emergence of chlorgraphynes (chlorinated graphynes) with variable Cl/C stoichiometry may be expected. Here, employing DFT band structure calculations, a series of new graphyne derivatives — layered chlorgraphynes — is examined on example of α-graphyne. The possible formation path of chlorgraphynes as a set of consecutive free-radical additions of Cl atoms is established. From examples of a few representative compounds, the trends in the structural and electronic properties are discussed, depending on their stoichiometry.