A 17-year-old boy and a 22-year-old man were followed and threatened by two young men near Amersham Railway Station.
Between 11.30pm and midnight on December 23, the pair first approached the 17-year-old boy who was leaving the station.
They followed him, repeatedly asked to go through his bag and to name himself, however, he managed to run away from them.
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Police believe the same men then punched a 22-year-old man in the face whilst attempting to take his phone near the junction of Bois Avenue in Chesham Bois.
The pair first asked the man for the time and when the man refused they looked to steal his phone.
Police describe the first offender as a white boy, approximately 5ft 10in tall and around 17 to 18-years-old.
He was wearing a black Nike balaclava, a dark coloured puffer jacket and dark trousers.
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The second offender is described by police as a white boy, roughly 5ft 9in tall and again around 17 to 18-years-old.
He was also wearing a black puffer jacket.
Emma Tarry, Communications Officer, Thames Valley said: "Anyone who may have information about either of these incidents should contact the police.
"You can contact us either making a report online or by calling 101 quoting reference number 43210578129.
"Alternatively, for 100% anonymity, you can also call the independent charity Crimestoppers on 0800 555 111."
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