We present the first results of the search of new halo and relic candidates in the NRAO VLA Sky Survey. We have inspected a sample of 205 clusters from the X-ray-brightest Abell-type clusters presented by Ebeling et al. (1996), and found 29 candidates. Out of them, 11 clusters are already known from the literature to contain a diffuse cluster-wide source, while in 18 clusters this is the first indication of the existence of this type of sources. We classify these sources as halos or relics according to their location in the cluster center or periphery, respectively. We find that the occurrence of cluster halos and relics is higher in clusters with high X-ray luminosity and high temperature. We also confirm the correlation between the absence of a cooling flow and the presence of a radio halo at the cluster center.