High-resolution neutron powder diffraction data have been collected on 6 perovskites of composition BaCe1-xNdxO3-x/(2), with 0 less than or equal to x less than or equal to 0.2, in which structural phase transitions Pmcn-->P4/mbm at x=0.05, and P4/mbm-->Pm3m at x=0.1, were inferred from a recent Raman spectroscopy study. Our results contradict these conclusions; for 0 less than or equal to x less than or equal to 0.16, BaCe1-xNdxO3-x/2 is orthorhombic, space group Pmcn. At x=0.2, the powder data are consistent with either space group Pmcn or Cmcm, and could not be distinguished using structural-model-free fits due to increased line broadening present in this sample. The smaller number of reflections in space group Pmcn favours this space group for x=0.2. The deviation from cubic symmetry has been determined from a calculation of the scalar spontaneous strain, assuming that the dopant-dependent effects in the thermal expansion properties are small in BaCe1-xNdxO3-x/2. The spontaneous strain decreases with increasing neodymium doping showing the deviation from an ideal cubic aristotype reduces with doping level. There is some evidence for saturation in the spontaneous strain at x>0.2.