It is unclear at this stage whether anyone has been injured.
The radio station has reportedly been broadcasting pro-freedom messages since Misurata fell into the hands of Libya's anti-government rebels last week.
Reports suggest that the bombing began in the early hours of this morning, and that a military aircraft thought to have been part of the attack has been shot down by anti-Gaddafi rebels.
The Financial Times has an eye-witness report from Misurata, which says that an aircraft was shot down while attempting to land at 4am.
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