The A2BX4family of K2SO4-related structures have long been of interest to crystal chemists, largely due to the numerous different polymorphs and complicated sequences of phase transitions they sometimes exhibit as a function of temperature. For most such A2BX4compounds, there are essentially only two distinct structure types or parent structures — a high-temperature, ‚hexagonal’ form isomorphous to α-K2SO4and a lower-temperature, orthorhombic form isomorphous to β-K2SO4. In addition to these two prototype structures, however, there often exist weakly distorted, or modulated, variants. In the case of the Ba2-xCaxSiO4system, five such modulated variants have been foundviaan electron diffraction study and characterized. The characteristic satellite extinction conditions associated with the weak satellite reflections have been used to determine displacement eigenvectors and atomic displacement patterns associated with each of the observed modulation wave-vectors. The widespread occurrence of modulated phases within the A2BX4family of K2SO4-related structures suggests an almost chronic instability to displacive modulation.