The private voicemails of princes William and Harry were both accessed by the now defunct News of the World tabloid owned by media baron Rupert Murdoch.
It is the first time the jury has heard that the Duchess of Cambridge's phone had been hacked.
In one message, William called Kate Middleton "babykins" and in another that he was almost shot with blanks, BBC reported.
An unnamed male also left a message for Prince Harry impersonating his then girlfriend Chelsey Davey.
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Former NoW editors Rebekah Brooks and Andy Coulson are on trial with five others accused of a number of offences, which they all deny, including conspiracy to illegally intercept voicemails.
In another message played to the court, Prince William said he was going "beagling", or hunting with dogs, and invited Kate to go with him.
A message from Prince William left on the duchess's phone was discovered at the house of Clive Goodman, then royal editor at the News of the World in 2006, prosecutor Andrew Edis told the Old Bailey court here.