The so-called House of Moray is a historiographical and genealogical construct to illustrate the succession of rulers whose base was at the region of Moray and who ruled sometimes a larger kingdom. It is much the same as Cenél Loairn (although not necessarily exactly), an originally Gaelic concept to express one of the two rivalling leader clans of early medieval Scotland.
The so-called house of Loairn or of Moray was distantly related to the Scottish House of Alpin, its rival, and claiming descent from the eponymous founder Loarn mac Eirc. Some of its members became the last kings of the Picts while three centuries later, two members succeeded to the Scottish throne ruling Scotland from 1040 until 1058.
At the times when the rival house held the throne, the Loairn leaders usually had their effectively independent state of Moray, where a succession of kings (kinglets) or mormaers ruled.
The Loairn succession followed quite loyally the rules of tanistry, resulting in practice to outcomes where branches of the leaders' extended family rotated on the rulership, possibly keeping a balance between important branches. This is quite typical for tribal societies, where primogeniture is much less usual than agnatic seniority or turns on the throne. For example, Macbeth, King of Scotland descended from one branch, and his stepson Lulach from another.
Not much nor convincing evidence survives that the House of Loairn followed in any way the postulated Pictish tradition of matrilineal succession. Rather, their succession seems to follow quite fully the Irish-Celtic tradition of agnatic clan.
Following kings of Dál Riata are recorded to have been members of the Cenél Loairn:
Cenél Loairn kings, in particular the descendants of Ferchar Fota, competed successfully for control of Dál Riata in the early 8th century, prior to the Pictish conquest of the kingdom by Óengus mac Fergusa.
Additionally, Giric mac Dúngail (878–889) may have been a member of this kindred.
Already MacBeth's father and cousin (Lulach's uncle) had been "kings of Alba":
Lulach's son and grandson were, however, titled kings of Moray, not of Alba:
Óengus of Moray (died 1130), who has no attestation of descending in male line from Cenel Loairn clan (he was son of daughter of Lulach), is the last known member of the kindred to have ruled Moray, after which it (supposedly) passed to William fitz Duncan of the Cenél nGabráin descended royal family. While the Meic Uilleim and MacHeths are sometimes associated with Moray, it is no longer widely supposed that they were claiming the Mormaerdom or that they belonged to this kindred, except possibly through female descent.