The heredity of the malignant blood disorders, leukemias, lymphomas and myeloma, has so far been largely unknown. The present study comprises genealogical investigations of one hundred and twelve Scandinavian families with unrelated parents and two or more cases of malignant blood disease. For comparison, one large family with related family members and three hundred and forty-one cases of malignant blood disease from the Faroese population was included. The inheritance is non-Mendelian, a combination of genomic parental imprinting and feto-maternal microchimerism. There is significantly more segregation in maternal than in paternal lines, predominance of mother-daughter combinations in maternal lines, and father-son combinations in paternal lines. Chronic lymphocytic leukemia is the most frequent diagnosis in the family material, and chronic lymphocytic leukemia has a transgenerational segregation that is unique in that inheritance of susceptibility to chronic lymphocytic leukemia is predominant in males of paternal lines. Male offspring with chronic lymphocytic leukemia in paternal lines have a birth-order effect, which is manifest by the fact that there are significantly more male patients late in the sibling line. In addition, there is contravariation in chronic lymphocytic leukemia, i.e. lower occurrence than expected in relation to other diagnoses, interpreted in such a way that chronic lymphocytic leukemia remains isolated in the pedigree in relation to other diagnoses of malignant blood disease. Another non-Mendelian function appears in the form of anticipation, i.e. increased intensity of malignancy down through the generations and a lower age at onset of disease than otherwise seen in cases from the Cancer Registers, in acute lymphoblastic leukemia, for example. It is discussed that this non-Mendelian segregation seems to spread the susceptibility genes depending on the gender of the parents and not equally to all children in the sibling line, with some remaining unaffected by susceptibility i.e. "healthy and unaffected", due to a birth order effect. In addition, anticipation is regarded as a non-Mendelian mechanism that can amplify, «preserve» these vital susceptibility genes in the family. Perhaps this segregation also results in a sorting of the susceptibility, as the percentage of follicular lymphoma and diffuse large B-cell lymphoma is lower in the family material than in an unselected material. Although leukemias, lymphomas and myelomas are potentially fatal diseases, this non-Mendelian distribution and amplification hardly play any quantitative role in the survival of Homo sapiens, because these diseases mostly occur after fertile age.