Measurements of the de Haas - van Alphen frequencies in Hg3-δAsF6 and Hg3-δSbF6 show that the Fermi surface of these compounds consists of cylinders with axes parallel to the c direction. A detailed model of the Fermi surface of these mercury linear-chain compounds is constructed for conduction electrons in the mercury chains. The cross-sectional areas of the Fermi-surface cylinders are accounted for by the Fermi-surface model. Cyclotron masses measured for some of the orbits are in satisfactory agreement with those predicted by the model. The excellent agreement between measured and predicted cross-sectional areas for both compounds shows that the model is valid for a range of values of the incommensurability parameter δ.