All cars:
At the Press Start screen, press X, Y, R, R, R, R, X, Y.
All game modes:
At the Press Start screen, press X, R, Y, R, L, R, R, R.
All extras:
At the Press Start screen, press L, R, X, L, X, R, X, Y.
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Demolition Racer: No Exit Cheats, Codes & Walkthrough/Guide/FAQ for Dreamcast from Cheat Code Central
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Demolition Racer: No Exit Cheats at CheatingDome.com.