The Duke and Duchess of Cambridge have met their baby nephew Archie

A royal representative told PEOPLE that the meeting took place in private after Catherine visited a secret WWII spy base in Bletchley Park, Buckinghamshire.

It's not known whether William and Catherine's children Prince George, five, Princess Charlotte, four, and 13-month-old Prince Louis joined them for the visit.

Harry and Meghan - who got married last year - announced that their baby son Archie Harrison Mountbatten-Windsor had been born in the early hours of May 6.

However, the new parents didn't introduce their little bundle to the world until two days later when they posed for a photo call and later revealed his name.

The 34-year-old prince said at the time: "Everybody says that babies change so much over two weeks so we'll be monitoring the changing process over this next month really. His looks are changing every single day.

"Parenting is amazing, it's only been two-and-half days, three days, but we're just so thrilled to have our own little bundle of joy and share some precious times with him as he slowly starts to grow up."

And flame-haired hunk couldn't resist bragging about his son and how well he'd settled into family life during his visit to Oxford Children's Hospital recently.

Amy, who was holding her 10-week-old baby daughter at the time of their conversation, said: "Harry asked me if she was over the stormy period as babies are supposed to be grumpy for the first 10 weeks - and she is. He said he's getting used to the baby and how Archie has fitted into family life. He said he just feels part of the family and he can't imagine life without his son."

And Meghan, 37, is equally besotted with her baby son as she gushed about his "calm" temperament during the photo call last week.

She said: "It's pretty amazing and I have the two best guys in the world so I'm really happy. He has the sweetest temperament, he's really calm. He's just been a dream, it's been a special couple of days."