The CaRMnSnO6 (R = La, Pr, Nd, Sm-Dy) double perovskites were prepared using a solid state reaction in evacuated sealed silica tubes at 1050-1100 degrees C. All compounds belong to the GdFeO3-type structure (orthorhombic a : b : c approximate to root 2a(p) : 2a(p) : root 2a(p) unit cell, space group Pnma, (a(+)b(-)b(-)) tilt system). The crystal structures were investigated by electron diffraction and high resolution electron microscopy and were refined from X-ray powder diffraction data for the R = La, Sm, Dy representatives (La: R-I=0.030, R-P=0.033; Sm: R-I=0.030, R-P=0.010; Dy: R-I=0.033, R-P=0.010). A disordered arrangement of the Ca and R cations over the A positions and Mn and Sn cations over the B positions was found in all cases. The small difference in charge and size between the Mn3+ and Sn4+ cations, the small degree of Jahn-Teller deformation of the MnO6 octahedra, and the ac-plane orbital ordering type were proposed as possible reasons for the cation disorder on the B sublattice. The compounds demonstrate a spin glass behavior in the temperature range from 25 to 300 K.