The initial period of rule by emperors had some short-lived dynasties during its beginning and towards the end. The Julio-Claudian dynasty (5 emperors) ended with a rebellion during which Nero had is assistant kill him as he did not manage to commit suicide and a civil war. The Flavian dynasty (3 emperors) ended with the murder of Domitian and the Nerva-Antonine (8 empeorors) dynasty ended with the murder of Commodus and also involved a civil war. The Severan(5 emperors) dynasty ended with the overthrow of Alexander Severus.
There was a 70-year period without dynasties. The emperors were generals appointed by their troops. The Constantinian dynasty ended because of murders of family members by Constantine's sons, wars between them and the death in battle of Julian. The Valentinian dynasty was replaced by the Theodosian dynasty via marriage and this last dynasty ended with murder and usurpation.