The court sentenced the three royals and two others to five years each, a sixth man for one year and handed down a 10-year term to a seventh man in absentia.
The royals include Sheikh Athbi al-Fahad Al-Sabah, a nephew of the Gulf state's emir and the former head of the secret service police.
He is also the younger brother of international sports figure Sheikh Ahmad al-Fahad Al-Sabah.
The defendants remain free on bail.
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Also convicted was Sheikh Khalifa Ali Al-Sabah, the editor of Al-Watan newspaper and television which were closed by the government for violating corporate finance rules in a decision ratified by the courts.
Another six men were acquitted.
The rulings are not final as they can still be challenged in the appeals and supreme courts.