The Roman Republic had a written Constitution which guaranteed certain rights to anyone who was a citizen. The main ruling body was the Roman Senate, composed of Patrician families ("old money" landed families.) The Senate elected Consuls. Normally, two Consuls were elected, and had veto power over Senate decisions and the power of Sacrosanctitas--their word was inviolable. There was also the Concilium Plebis comprised only of Plebians (lower class citizens) with control over domestic affairs; Tribunes, who protected the rights of the plebians; and a Censor, the most powerful man in the Republic. He was elected every five years, enrolled new Patrician families into the Senate, and prosecuted Senators for corruption. Finally, there was a Pontifex Maximus,a chief priest who was responsible for the official calendar. He determined which days were appropriate for the conduct of business, and also the dates for movable feasts. In the event of national emergency, the Constitution provided for the appointment of a Dictator who held absolute authority for a period of six months. This provided for stability during times of national crisis.
Although the Senate remained extant during the Empire, the primary source of authority was the Emperor, who held absolute authority. Julius Caesar, the first Emperor, was first Dictator, and was assassinated because it was believed he wished to be King. Augustus, who followed, did not make this mistake, and called himself Princeps, (first citizen) and took great pains to portray himself as "just another Roman citizen." The office of Emperor was NOT passed automatically from father to son, although on occasion this did happen. The Emperor normally named his own heir, who took the title of "Caesar," while the Emperor retained the title of "Augustus." The true power behind the Emperor, however, were the Praetorian Guard, his personal bodyguards. If the Praetorians did not approve of a candidate, or no longer supported a sitting Emperor, his days were normally numbered. The support of the Army was also important. During the last days of the Empire, there were multiple claimants to the Purple Robe (which only the Emperor wore) when the armies they commanded proclaimed them Augustus. For more information, a good source is How Rome Fell; Death of a Superpowerby Adrian Goldsworthy.