Front end wobble.
This problem is part of the Colonial Cruiser and Speedmaster lore.
Check list:
1) Is the front tire properly inflated? Member shagga wrote "My TBA (fitted with Bridgestones) does that sort of stuff when the front tyre pressure gets below 30psi. When I put in 32psi or above it handles perfectly. Check the easy things first."
2) Cupped front tire.
3) Wheel balance
4) Rim truing
5) Steering head adjustment/lube/bearings
6) Rear tire alignment
