The Fermi surfaces of Pb1-xSnxTe in the cubic and rhombohedrally distorted phases for both normal and inverted band structures have been investigated using the Shubnikov-de Haas effect. Comparison of the observed Fermi-surface cross-sectional areas with the band structures of Dimmock (1981), for the cubic phase, and of Bangert (1981), for the rhombohedral phase, yield parameters which are in agreement with values established previously for the cubic phase. The complex character of the Fermi surfaces at the points T and L in the rhomobohedral Brillouin zone is found to agree with the predicted splitting of the ellipsoids of the cubic phase into the 'skin' and 'core' of an apple-like composite surface, originating in the lifting of the inversion symmetry of the structure in the structural phase transition. Clear evidence is obtained for the presence of structural domains in the rhombohedral phase. The carrier concentrations deduced from the Fermi-surface volumes are found to agree with those measured from the weak-field Hall coefficients, when account is taken of the anisotropy of the multiple carrier valleys in the band structure.