A parallel cousin is a first cousin who is paternal uncle's child or maternal aunt's child, while a cross cousin is maternal uncle's child or paternal aunt's child. The distinction between Cross Cousins and Parallel Cousins is important in traditional societies. Parallel cousins are not the subject of promoted marriage since a union in many cultures would fall under an incest taboo. In societies that differentiate between cross-cousins and parallel cousins, cross-cousin marriage is usually preferred or sometimes even obligatory.
Some societies consider first-cousin marriages to be ideal. Parallel cousin unions in some cultures would fall under an incest taboo, since parallel cousins are part of the subject's unilineage whereas cross-cousins are not. Maynard Smith in 'The Evolution of' Sex notes that Richard D. Alexander suggested that paternity uncertainty may help account for the intermarriage taboo on parallel, but not on cross cousins. In consanguineal kinship in anthropology, a parallel cousin is a cousin from a parent's same-sex sibling, while a cross-cousin is from a parent's opposite-sex sibling. In in Unilineal Descent, the genetic kinship is near-total. In a patrilineage, parallel cousins are part of the subject's unilineage whereas cross cousins are not.
In matrilineal societies, parallel cousins are considered to be related to the subject while cross cousins are not. Parallel cousins, the children of one's father's brother or one's mother's sister, are treated as brothers and sisters. They are treated with the same avoidances as real brothers and sisters. Like true brothers and sisters, they are referred to with the terms tuakaqu (an older brother or sister) and taciqu ( a younger brother or sister). The role of cross-cousins is important in some cultures. Marriage is promoted between cross-cousins in the Iroquois system.
Parallel cousins are the subject of promoted marriage. The preferential marriage of a male to his father's brother's daughter, common among some pastoral peoples. Parallel cousin marriages help keep property within a lineage.
In many "classificatory" systems of kinship terminology, relatives far beyond genealogical first cousins are referred to using the terms for parallel cousins and cross cousins. In many other "classificatory" systems, parallel cousins (though not cross cousins) are also referred to by the same terms that are used for siblings.
Fathers who are also brothers may overtly or covertly share sexual relations with the wife of one or the other, raising the possibility that apparent parallel-cousins are actually half-siblings, sired by the same father. Likewise, mothers who are also sisters may overtly or covertly share sexual access to the husband of one or the other, raising the possibility that apparent parallel cousins are actually half-siblings, sired by the same father. - Maynard Smith, J. (1978) The Evolution of Sex. Cambridge University Press.