Marx posted several photos on his Facebook and Twitter pages showing the incident during the flight from Vietnam to Seoul, South Korea on Korean Air.
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Marx's wife, model and television host Daisy Fuentes, captured the entire incident. She said the suspect was sitting in the next row to them when he suddenly started attacking the flight attendants and passengers.
Fuentes wrote on social media that it went on for four hours.
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One flight attendant was armed with a Taser, which the couple said she didn't know how to use.
They said the man was initially restrained but then managed to break free before he was tied up again.
Marx said the crew was not properly trained and ill-equipped for the situation, and said one crew member and two passengers were hurt.
Police boarded the flight as soon as they landed in Seoul and took the suspect into custody, Marx said.