RNLI Selsey Lifeboat Station said the owner of a 27ft motorboat called UK Coastguard after an oil pipe fractured, 'spraying oil over the engine'.
A spokesperson said: "The vessels position was approximately 300 metres south of Bognor Pier and the owner feared running aground on Bognor rocks or hitting the pier.
"At the request of the Coastguard the Selsey all-weather lifeboat (ALB) launched at 3.25pm and headed towards the given position.
"At 3.44pm the lifeboat arrived on scene to find the two persons on board the vessel had managed to deploy the anchor, unfortunately directly above Bognor rocks and with the tide going out they needed to be pulled clear before the tide dropped more exposing the rocks."
The motorboat had 'recently been purchased' and was 'on passage from Cowes I.O.W to Brighton Marina'.
A lifeboat crewman was transferred to the vessel to 'assist with the retrieval of the anchor' and set up the tow.
The spokesperson added: "After consultation with the Coastguard, Littlehampton Harbour Master, and the Littlehampton RNLI, it was decided to tow the motorboat to a position one mile south of Littlehampton and anchor the vessel as the tide was too low to get into the harbour.
"Littlehampton Lifeboat were training later on in the evening and agreed to go out at 9pm and assist the motorboat into harbour.
"At 4.50pm the casualty vessel was anchored off Littlehampton and the lifeboat crewman was recovered to the lifeboat.
"The lifeboat was released from the incident to return to Selsey. The lifeboat arrived back at 5.40pm and was recovered a short while afterwards."
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