The best option would be to soak the frame in an oxalic acid bath. There are lots of threads on its use. Here's one: The Wonders of Oxalic Acid. That will remove the rust, but the exposed frame will rust again unless it's covered up (say, with black touch up paint, or clear nail polish, for example). Another option, if you do not want to strip & soak the frame, is some careful application of naval jelly in the rust spots. It can damage the paint, so you may try applying it with a brush just to the areas where the paint has been replaced by rust.
'70 Cilo Pacer | '73 Ron Kitching/Speedwell Ti | '74 Nishiki Competition | '74 Peugeot UE-8 | '86 Look Equipe "Bernard Hinault" (Reynolds 753) | '89 Park Precision (Team ParkPre/Conejo Velo issue) | '90 Park Precision MTB (Team ParkPre/Conejo Velo issue)
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This is a nice score. An USA-made Trek 930 with lugs. The rust is surface only.
The choice of remedy depends on how much this bike is worth to you.
If you want to restore it then oxalic acid bath is the best results.
If you only want to arrest the rusting and ride the bike, a beater or commuter, then wire brush/naval jelly the rust spots till the rust is gone, and spot prime and paint the areas. Another option is to buy rust neutralizer at the auto parts store. Carefully brush it onto rust spots and it'll convert the rust to inert state, then paint over it.
A Trek 930 is a worthy frame to save. Tru-Temper Cr-Mb DB tubing throughout.
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I prefer Citric Acid Powder for my rust removal projects. Much less toxic to handle / dispose. Does the same job.