The statements, carried by the official Saudi Press Agency, said the convicts were executed in the northern al-Jof region.
The first said that a Saudi citizen, Burhan al-Shammari, shot and killed countryman Daifullah al-Sharari following a fight. The second one said Safwan Zuhaifi, from Yemen, "kidnapped and raped a youth by force." It did not give the youth's age or nationality.
Saudi Arabia follows a strict interpretation of Islam under which people convicted of murder, drug trafficking, rape and armed robbery can be executed. Beheadings are carried out with a sword in public.
Tuesday's executions brought to 76 the number of people, including two women, beheaded in the kingdom this year. The kingdom beheaded 38 people last year and 83 people in 2005.