--Blood group opinions based on the gene systems and characteristics usual in the FRG are able to exclude about 93% of all non-fathers. With additional systems, including the HLA system, this can be increased to between 98 and 99%. 2. --Owing to repetition, additional systems hardly improve exclusion efficiency. But each and every system is useful for positive biostatistical proof. 3. --As a rule, a computer is necessary for the biostatistical evaluation of blood group findings in cases involving aliens, deficiency, brothers, and incest. The same holds for the evaluation of HLA findings, particularly if one wants to take account of the recombination rate between locus A and B. 4. --The W-value obtained on the basis of Essen-Möller's formula contains all the information necessary for a biostatistical evaluation of triplet cases. In all other cases the method of calculation must also be based on Bayes' Theorem, if necessary with the support of Bayes' Postulate, i.e. with a neutral a priori of 0.5 as a rule [5]. Decisions limited to probably values serve little purpose in court cases.