The recently developped theory of MINQUE and r-MINQUE estimators is applied to a special class of probleii-1s arising for example in the chamical industry if a certain mea-suring arrangement is recovered repeatedly by values. From the mathematical point of view, the question concerns compensation problems where, however, the weights are unkniiwn in contrast to tho classical conpensation calculus. The treatment of such a problem with repeated recovering by value is reduced to the essentially less extensive treatment having only simple recovering. Under natural assumptions it is shown that the MINQUE as well as r-MINQUE estimators are asymptotically normally distributed. Crit.eria for the existence and for n particular property of tlhe solution allowing simpli-fications of the calculation are given. They are easily applicable.