Police said the pair tried to snatch a 16-year-old girl's phone in Pontefract Park between 12.50pm and 1.15pm yesterday (Wednesday).
Their first victim managed to run away with her property.
In a second incident between 1pm and 2pm the moped thieves grabbed a phone from another 16-year-old female.
West Yorkshire Police said the suspects were both white and wearing helmets and camouflage jackets.
Detective Inspector Dave Rogerson, of Wakefield District CID, said: “These incidents are clearly linked and while the victims were not injured what has happened has clearly caused the young ladies involved some distress.
“I would urge any member of the public who witnessed these incidents to contact police."
Information can be passed to the police by calling 101.