It is not clear how closely related Sheikh Talal is to Emir Sheikh Sabah
Reports from Kuwait say a member of the ruling family has been sentenced to death for drug trafficking.
Correspondents say it is thought to be one of the first times that such a sentence has been given to a member of the ruling Sabah family.
Sentencing Sheikh Talal Nasser al-Sabah to death, the judge said he had "willingly walked the path of evil".
It was not immediately clear how closely related Sheikh Tala is to senior members of the ruling family.
The judge in the case said Sheikh Tala's crimes had "threatened society... especially young people", a Kuwaiti newspaper reported.
He was also fined US $35,000 dollars.
Sheikh Talal was convicted of trading in hashish, money laundering and the illegal possession of weapons, press reports said.