Two crystal structures of ethylene (a= 12.272(2) ${AA}$) and acetylene (a = 12.245(2) ${AA}$) sorption complexes of dehydrated fully $Ca^{2+}$-exchanged zeolite A have been determined by single crystal X-ray diffraction techniques in the cubic space group, Pm3m at $21(1)^{circ}C$. Their complexes were prepared by dehydration at $360^{circ}C$ and $2{ imes}10^{-6}$ Torr for 2 days, followed by exposure to 200 Torr of ethylene gas and 120 Torr of acetylene gas both at $24^{circ}C$, respectively. The structures were refined to final R (weighted) indices of 0.062 with 209 reflections and 0.098 with 171 reflections, respectively, for which I > 3${sigma}$(I). The structures indicate that all six $Ca^{2+}$ ions in the unit cell are associated with 6-oxygen ring of the aluminosilicate framework. Four of these extend somewhat into the large cavity where each is coordinated to three framework oxide ions and an ethylene molecule and/or an acetylene molecule. The carbon to carbon distance in ethylene sorption structure is 1.48(7) ${AA}$ and that in acetylene sorption structure 1.25(8) ${AA}$. The distances between $Ca^{2+}$ ion and carbon atom are 2.87(5) ${AA}$ in ethylene sorption structure and 2.95(7) ${AA}$ in acetylene sorption structure. These bonds are relatively weak and probably formed by the electrostatic attractions between the bivalent $Ca^{2+}$ ions and the polarizable ${pi}$-electron density of the ethylene and/or acetylene molecule.