From a local estate sale, two vintage Indianapolis Motor Speedway / Indianapolis 500 drivers caps. Both are white cloth, lined, one size with velcr closure, machine stitched, with some soiling especially along sweat band inside. One looks like it has make-up soiling it.
Based on the designs, these 2 Indianapolis 500 racing caps likely date back to the 
late 1980s or 1990s.One AI site suggested the 1970s.
Reasoning:
These caps have a snap, reminding me of chauffeur's caps but can also be called drivers caps or racing caps due to their historical connection with motor racing and the Indy 500. White background.