The Canadian kinship system has been traditionally viewed as consisting of isolated nuclear family units in a bilateral or symmetrically multilineal structure. An analysis of the kinship networks of rural and urban Icelanders and Jews in Manitoba supports the hypothesis that the structure of the families in these groups exhibits a matrilateral bias. Evidence is presented which indicates that the bias is inherent in the system due to the close ties between mothers and daughters, a condition which leads to gynocentricity, i.e., closer ties between female members of the extended family. The results of the analysis also reveal that the sex-role behavior of the nuclear family heads is related to the strength of bias as displayed by the various family units. In the families in which one head performs activities traditionally defined as being in the realm of the opposite sexed head, the interaction becomes skewed towards the extended families of the individuals involved in the "role-crossover". We also find that continuity in the role behavior of the males is related to the strength of the bias. In the families in which a family corporation or business enterprise exists, we find that the strength of the matrilateral bias, is less than in the families in which sons do not succeed their fathers in occupational activity. Finally evidence is presented which indicates that the nuclear family may not be the isolated unit as has been conceived by many social scientists concerned with the family in industrial society.