Both are sons of former President George Herbert Walker Bush, who was beaten by Bill Clinton in 1992. And George W (everybody calls him George double u) may yet revenge his father by standing for the Republican nomination for President in 2000, though he has yet to declare his intentions. Opinion polls yesterday showed him beating Al Gore, the most likely Democratic candidate, by 57 per cent to 39 per cent, a handsome margin.
George W beat his Democrat opponent, Garry Mauro, by a 2-to-1 margin to win the first ever back-to-back four years terms. On his coat tails rode his new deputy, Rick Perry, a Republican, and the party also scooped at least six of the seven top statewide posts and all judicial seats - the most offices the Republicans have held in recent years. He fought a clean fight, unlike candidates elsewhere, and attracted plenty of Democrat support.
But the family seemed to have a deeper significance for the Republican Party, one that was attracting favourable comment yesterday. Both are conservatives, but both are on the moderate side of the party. Strikingly unideological, fixing their sights on education as the key issue, both won support from across the political and ethnic spectrum.
On a night when right-wing Republicans performed poorly - notably Lauch Faircloth from North Carolina, who lost his Senate seat - a kinder, gentler vision of the party was on show. Both are young - George W is 52, his brother 45. They are the first fraternal team to hold two governorships since Nelson Rockefeller and his brother Winthrop held New York and Arkansas.
Neither is keen to showcase their lineage to the former President, though George said yesterday that "it helps to have a good mom and dad". Barbara Bush, the former first lady, is a figure of huge respect in the Republican Party and in the country at large, and it is to her, rather than his father, that George W refers to frequently on his campaign trips.
But both parents were elated yesterday. "I cannot possibly begin to express the joy that Barbara and I have in our hearts, nor the pride we have in George and Jeb," the former President said.
George W hinted at broader ambitions in his acceptance speech, and also at criticism of the Congressional Republicans, who have been strikingly ideological. He said the result showed "that a leader who is compassionate and conservative can erase the gender gap, open the doors of the Republican Party to new faces and new voices. It says someone who is conservative and compassionate can win without sacrificing principles".
His brother joined in. "This is a victory for doing things a new way and I'm excited about that. This is a victory of inclusion rather than exclusion," Jeb said in Florida.
Their appeal to Hispanic voters sets them apart in the Republican Party. The Hispanic population is growing fast, and the party needs to appeal to it in Texas, in the South-west and in California if it is to build a coalition not just for the next Presidential election, but for the coming decades. Both speak and campaign in Spanish, a big asset.
George W has said that he will decide in the spring whether or not to stand for President. There is speculation in political circles that like Mr Clinton, he may have shadows in his past that would make him an easy target for the press and his opponents, but he denies this. The main considerations, he says, are whether or not to leave Texas, and the impact on his family of living in the "bubble" - something his family have surely become more accustomed to. He admits that he had a problem with alcohol but gave it up five years ago.
The other risk he must confront is that the Republican Party is dominated, amongst the activists, by movement conservatives from the Christian fundamentalist right who will subject him to some very severe tests. He opposes abortion but refuses to interfere in the legal rights of individuals - something that will cost him dearly. The Republican right is sceptical of a man who comes from a patrician lineage and who espouses a more moderate line. Mr Bush may have to take a more conservative position if he is to win the Republican primaries in 2000, perhaps by choosing a more conservative running mate.
However, the twin victories have also triggered a more amusing idea in the US press. "We don't want Jeb lurking around, trying to clamber onto the ticket in 2008," wrote Maureen Dowd in the New York Times. "Maybe we should just go the whole hog with a sibling-rivalry Bush-Bush ticket, leaving it to George W and Jeb to scrap over who gets top billing."Reuse content