The ruler of England was King William I (William the Conqueror), who had ruled since 1066 and would continue to do so until 1087.
The ruler of Gwynedd at the beginning of 1081 was King Trahaearn ap Caradog, who had ruled since 1075. This year, King Gruffydd ap Cynan would take over.
The ruler of Moray at this time was likely to have been Mormaer Máel Snechtai mac Lulaich.
The ruler of Scotland was King Malcolm III (The Great Chief), who had ruled since 1058 and would continue to do so until 1093.