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.
Moscow is trying to stop Balkan countries from entering NATO. Greece eventually took measures against Russia, even though Greek Prime Minister Alexis Tsipras had earlier said that Russia was Greece's strategic partner
The Ukrainian government refuses to abode by its obligations, rejects a peaceful resolution of the conflict, and disregards its own people, the president said