The structural features of the Sr2Nd1−xCaxCu2O5+yF1+&dgr;(0⩽x⩽1) oxyfluoride system have been investigated by electron diffraction and high resolution electron microscopy. The short-range-order (SRO) state has been observed in the Sr2Nd0.5Ca0.5Cu2O5+yF1+&dgr; oxyfluoride (Tc≈70 K). This kind of SRO structure can be understood in terms of the ordering of insertion of fluorine and/or oxygen atoms located between the SrO(F) double layers. The most probable ordering scheme is proposed. The effects of Ca content on this kind of SRO state as well as other locally ordered states have also been investigated.©1997 American Institute of Physics.