The R10 and R11 late blight differentials of Black (tetraploid clones 3681ad1 and 5008ab6) were crossed with the susceptible potato (Solanum tuberosum) cultivar Maris Piper and the progeny were assessed for blight resistance in a whole plant glasshouse test using race 1,2,3,4,6,7 of Phytophthora infestans. The disease scores for the R10 population displayed a continuous distribution whereas the progeny in the R11 population could be categorised as resistant or susceptible. A bulk segregant analysis using amplified fragment length polymorphism assays was done on the ten most resistant and ten most susceptible progeny in each population and two closely linked markers were found to be associated with resistance. R11 mapped to 8.5 cM from marker PAG/MAAG_172.3 and R10 mapped as a quantitative trait locus in which marker PAC/MATC_264.1 explained 56.9% of the variation in disease scores. The results were consistent with R10 and R11 being allelic versions of genes at the R3 locus on chromosome 11. The implications are discussed for mapping R-genes which fail to give complete immunity to a pathogen.