what zoom lenses will work on a pentax ME 35mm camera?

You still have a good working Pentax ME? That thing’s got to be about 25-30 years old! Good for you! Any lens that has the Pentax K mount should work just fine. You can find them almost anywhere. I found a perfectly good working 200 MM lens at a Goodwill shop! Look for the PK mark somewhere around the mount ring. Many of the aftermarket companies also make some fine lenses for Pentax. Tamron comes immediately to mind. Also, on a budget, Ritz Camera’s, Quantaray brand makes an acceptable lens.

any Pentax mount lens will work (like the previous responder said) with exception of the newest series (DA and the FA-J series) wich do not have an aperture collar on the lens.