Starting with a BST (Ba0.6Sr0.4TiO3) nanopowder with a mean diameter of about 50 nm, the average grain size increases from the nanometer to the micrometer range (from 70 nm to 1-2 mum) by thermal annealing between 700 and 1400degreesC.The dielectric properties of these pressed powders has been determined, showing that the temperature of transition decreases with grain size. In order to check this evolution in dense ceramics in which the grain size is conserved, composite materials based on ferroelectric nanograins and a non-ferroelectric matrix have been prepared. Core-shell composites with different core sizes (150 and 50 nm) were synthesized in this way and the results obtained confirmed the decrease of the transition temperature with grain size, from 290 to 230 K respectively. Furthermore, dielectric losses are very weak in these core-shell composites-at between 0.1 and 1 % in the temperature range 150-450 K and the frequency range 1 X 10(3)-1 x 10(5) Hz. Ferroelectric nanograins of BST were also incorporated into silica gel for comparison with the core-shell materials. Even for a high fraction of BST (approx. 75 %), the properties of the grains are masked by the presence of silica, which possesses a very low dielectric constant. This study has allowed the possible determination of the macroscopic dielectric properties in nanostructured ceramics.