Complex characters of plants such as starch and sugar content of seeds, fruits, tubers and roots are controlled by multiple genetic and environmental factors. Understanding their molecular basis will facilitate diagnosis and combination of superior alleles in crop improvement programs ("precision breeding"). Association genetics based on candidate genes is one approach toward this goal. Tetraploid potato varieties and breeding clones related by descent were evaluated for 2 years for chip quality before and after cold storage, tuber starch content, yield and starch yield. Chip quality is inversely correlated with tuber sugar content. A total of 36 loci on 11 potato chromosomes were evaluated for natural DNA variation in 243 individuals. These loci included microsatellites and genes coding for enzymes that function in carbohydrate metabolism or transport (candidate loci). The markers were used to analyze population structure and were tested for association with the tuber quality traits. Highly significant and robust associations of markers with 1-4 traits were identified. Most frequent were associations with chip quality and tuber starch content. Alleles increasing tuber starch content improved chip quality and vice versa. With two exceptions, the most significant and robust associations (q < 0.01) were observed with DNA variants in genes encoding enzymes that function in starch and sugar metabolism or transport. Comparing linkage and linkage disequilibrium between loci provided evidence for the existence of large haplotype blocks in the breeding materials analyzed.