Two brothers
Three brothers, Adam, Hoss and Little Joe.
If you mean in the TV show Bonanza then there were originally three brothers. (Adam, Hoss, and Little Joe) In later seasons however, after Pernell Roberts quit the show, Ben adopts an orphan named Jamie, so there are technically four Cartwright brothers.
Joe, Eric, Adam
There was Adam Cartwright played by Pernell Roberts, Eric "Hoss" Cartwright played by Dan Blocker, and Joseph Francis Cartwright a.k.a Little Joe Cartwright played by Michale Landon.
Adam Cartwright and Little Joe Cartwright
The beautiful Paint Little Joe Cartwright rod was named Cochise.
Joseph 'Little Joe' Cartwright played by Michael Landon. Eric 'Hoss' Cartwright played by Dan Blocker. Adam Cartwright played by Pernell Roberts. (He quit the show in 1965 and was not replaced). Ben Cartwright had one adopted son also, Jamie.
On the TV series Bonanza the three sons of father Ben Cartwright were Adam Cartwright , Eric "Hoss" Cartwright and "Little" Joe - Joseph Cartwright .
The character Little Joe did not die on the tv series Bonanza. He was the only of the brothers to marry during the regular tv series. Michael Landon, the actor who played Joe Cartwright, died years later (July 1, 1991) suffering from pancreatic cancer. http://en.wikipedia.org/wiki/Little_Joe_(character)
The Oath
The character who lived at The Ponderosa was called Little Joe Cartwright.
Bonanza - 1959 Alias Joe Cartwright 5-17 was released on: USA: 26 January 1964