My oldest bike, is my mother's 1944 Western Flyer...knockoff that I use for yard art. I had to replace the wheels, as the originals had rusted through where they had rested for so many years. They are also yard art, but could no longer support the weight of the bike.
The oldest rideable bike is my 1984 Raleigh Rapide Mixte. The frame, fork, headset, and derailleur hanger are original. The rest is a more modern 2x10 mixture of microshift/105. It was originally a drop bar bike.
