BBC News
Abdulkarim Ali Abdulkarim and Hani Ahmed Deen Mohammed were accused of handing over sensitive information over a period of more than 10 years.
Few details were given about the men's background, but one was said to be the owner of a printing press and the other a secretary working for the coastguard.
The men's lawyer told AFP news agency they will appeal against the verdict.
A third defendant, Iskandar Abdo, was acquitted for lack of evidence.
The three were arrested in the southern city of Aden in June last year for "illegal contact" and went on trial in October.
Media barred
Court proceedings have been held behind closed doors after the media were barred from covering the trial.
But according to the charge sheet, the men handed over "information, documents and photos relating to military secrets and the country's political, security and economic situation, to the detriment of Yemen".
Their lawyer, Shadha Mohammed Nasser, told AFP that the two received their death sentence calmly, although they considered it "unjust" and were counting on the appeal.
