Cabinets have been overpaiinted several times
Lightly sand them so the paint will stick
Hi Terri. If you don't want to spend days and days stripping and sanding your cabinets, you could try a new paint on the market. It's called Beyond Paint. It eliminates the need of stripping, sanding, priming. or sealing. It's a bit pricey though. Home Depot sells it for approx. $100 per gallon.
Terri: I would also sand them. ...and do a good, complete job.
Nothing like a clean stripped pallet to get a good paint job.