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We develop Hachemeister's regression model 111 credlbihty theory (without proofs) and indicate how the involved structural parameters can be estimated from the observable variables (with proofs for the simple results and those not yet published).Large famlhes of unbiased estinaators are available. From the practical viewpoint this is rather a handicap because it creates the problem to decide what estimators actually to use. In order to fix optimal estimators, we adopt the small-sample critermn of minimum-variance But in the research for general solutmns three kinds of difficulties arise.(i) The calculations become too lengthy. (fi) The optimal estimators depend on some of the parameters to be estimated (Then we call them pseudo-estimators). (ill) The optimal estimators depend on new structural parameters defined in terms of fourth-order momentsOnly a compromise allows to cope with this reahty. Sltuatmn (ill) creates new estimation problems. They can only be avoided at the cost of the Introduction of special assumptions or approxiinatlons. Then problem (i) is more or less automatically solved. By an obvious method of successive approximations pseudo-estmlators can serve as true estimators. Thus (li) is no real problem. GENERAL NOTATIONS AND DEFINITIONS MatricesThe same main symbol is used to denote a matrix c and its elements c{. Here c{ is the element at the intersectmn of row i and column j. The row i is denoted by c, and the column j by d. When the number of rows is m and the number of columns n, we say that the matrix has dimensions n (m)-