Results from radiographic screening for canine hip dysplasia (CHD) and elbow dysplasia (CED) of 48 367 German shepherd dogs born in 2001–07 were used for the population genetic analyses. Available information included CHD scores for 47 730 dogs, CED scores for 28 011 dogs and detailed veterinary diagnoses of primary ED lesions for a subsample of 18 899 dogs. Quasi-continuous traits were CHD, CED and cases of CED without radiographically visible primary lesion (CED-ARTH). Binary coding was used for fragmented medial coronoid process of the ulna (FCP), borderline findings and mild to severe signs of dysplasia in hip and elbow joints. Genetic parameters were estimated in univariate threshold and multivariate linear and mixed linear-threshold models using Gibbs sampling. Correlations between univariately predicted breeding values (BV) indicated genetic differences between borderline and affected disease status for both CHD (rBV = 0.5) and CED (rBV = 0.3). Multivariate genetic analyses with separate consideration of borderline findings revealed moderate heritabilities of 0.2–0.3 for the quasi-continuous traits with positive additive genetic correlation of 0.3 between CHD and both CED and CED-ARTH. For FCP, heritability of 0.6 and additive genetic correlations of +0.1 to CHD and −0.1 to CED-ARTH were estimated. Results supported the relevant genetic determination of CHD and CED, argued for both diseases against interpretation of borderline findings as healthy and implied genetic heterogeneity of CED. Accordingly, future breeding strategies to reduce the prevalences of CHD and CED in the German shepherd dog should be most efficient when based on BV from multivariate genetic evaluation for CHD, CED-ARTH and FCP with use of the whole scale of categories for classification of CHD and CED.