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.
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The defendants remain free on bail.
They were among 13 people charged with using WhatsApp and Twitter to insult the emir and publish false news accusing judges of accepting bribes, the court ruled.
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.