A number of transition metal oxide materials, both new and previously reported, have been synthesised, their structures based on the n = 2 Ruddlesden-Popper layered perovskites. Their structures were determined through Rietveld refinement against X-ray and neutron powder diffraction, supported by vibrating sample magnetometry and thermal analysis. The structure of the double layered phase Gd2SrCo2O7 was determined in the temperature range 300 – 973 K by refinement of powder neutron diffraction data. The room temperature structure is tetragonal, and displays small tilts of the oxygen sublattice that are described by a 2a0 2a0 x c supercell model in the space group P42/mnm rather than the idealised Sr3Ti2O7 I4/mmm structure as previously reported. A structural transition at ~ 580 K is characterised by reduction in the unit cell symmetry and distortion of CoO6 octahedra; the behaviour is concurrent with a spin crossover in the Co (III) ions from intermediate to high spin. The structure of the new phase Nd2BaCo2O7 was determined in the temperature range 298 – 873 K by refinement of powder neutron diffraction data. At all temperatures, the structure is metrically tetragonal, however the octahedral rotations are best described in the orthorhombic space group Bbcb, with a = b = 2a0. The structures of the phases Ln2SrFe2O7 (Ln = La, Nd, Gd) have been determined by refinement of variable temperature powder neutron diffraction data. At room temperature all the materials crystallise in the tetragonal space group P42/mnm, isostructural with the phase Tb2BaFe2O7. On heating, the gadolinium and neodymium phases undergo transitions to lower symmetry; the octahedral tilts of the high temperature phases are best described in the space group Bbmm. The new phases Nd2-xSr1+xFe2-xO7 have been prepared and their structures determined by Rietveld refinement of room temperature powder neutron diffraction. All the materials crystallise in the tetragonal space group P42/mnm. The degree of octahedral tilting decreases as x increases, indicating a reduction of compression of the perovskite lattice as the average A-site cationic radius increases. The phase Sr3CoNbO7 has been prepared and its structure determined by refinement of powder neutron diffraction data. At room temperature and 3.4 K there is no evidence of magnetic ordering, B-site cationic ordering or octahedral tilting. The material is isostructural with the undistorted Sr3Ti2O7, which implies that the spin state of Co (III) in the material is low spin. The material Sr3Ti2O7 was prepared and its structure determined in the temperature range 298 – 1073 K. At all temperatures, the structure is tetragonal, with no rotations of octahedra. Unit cell parameters and bond lengths expand smoothly over the temperature range.