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In heavy 3-quart saucepan, melt butter over low heat. Stir in flour. Cook 3 minutes, stirring constantly.
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Stir in broth; heat to boiling. Boil 2 to 3 minutes, stirring constantly, until mixture is thick and smooth.
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Reduce heat to low. Add cheese, 1 cup at a time, stirring over low heat until cheese is melted and mixture is smooth.
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Pour cheese mixture into a fondue pot or a little crockpot; keep warm over low heat.
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Serve with various dippers - French bread cubes, crackers, or vegetables.