Police said the first incident happened late on Tuesday (August 25) while the second happened in the early hours of Wednesday (August 26).
That first incident concerned reports of men in possession of knives in North Trade Road, police said.
The suspects left the area in a vehicle, which was stopped by police nearby, according to police.
A police spokesman said: “The driver – a 19-year-old man from Battle – was arrested on suspicion of being concerned in the supply of a Class B drug.
“The passenger in the vehicle fled the scene and enquiries are ongoing to locate him.”
As NPAS was already in the area, it was called to assist with a second incident whereby a vehicle travelling at excessive speed in Battle High Street failed to stop for police.
The helicopter tracked the vehicle to Plough Lane in Hastings, where police attended and arrested a 20-year-old man from Bexhill, police said.
A spokesman for the force said he was arrested on suspicion of driving dangerously, going equipped for theft of a motor vehicle, taking a motor vehicle without the owner’s consent, theft of a motor vehicle, driving without insurance, failing to stop when required by police, and possession of a pointed bladed article.
He remains in custody at this time, police added.
Police are treating both incidents as ‘isolated matters’ and enquiries are continuing.