For a Republic, the United States loves dynasties. The Bush dynasty is likely to have a Presidential candidate in the election next year and the newer dynasty – the Clintons – will also have their own favoured daughter running for President.
Although in theory anyone born in the United States can become president of that nation in reality you need a great deal of money, a great deal of influential support (money buys that) and a familiar name.
If a republic gets to choose its leaders from a couple of political dynasties then that is neoether republican nor democratic. The trend seems to followed in the United Kingdom where familiar dynasties are beginning to emerge.