The Swedish State Institute for Blood Group Serology is a central government laboratory handling all blood typing in paternity cases in Sweden, each year testing 1,500-2,000 cases using about 13 polymorphisms. Of the accused men, 35%-40% are nonfathers, but in one-man cases (about 78% of all cases), approximately 75% are the true fathers. Exclusions appear to be distributed as expected from allele frequencies, and the paternity probability of nonexcluded men is assessed with a Bayesian approach. Some cases are retested in extended investigations which raise theoretical exclusion capability from about 87% to about 99%. Both the results of extended investigations and the theoretical consideration of the distribution of paternity probabilities support the use of such positive statistical evidence for the attribution of paternity.