Preheat oven to 450 degrees F (230 degrees C). Grease one 8×12 inch baking dish.
Bring a pot of salted water to a boil. Add potatoes; cook until tender but still firm. Drain, and transfer to a large bowl to cool.
In a mixing bowl, combine sweet potatoes, bananas, white sugar, brown sugar, pecans, evaporated milk, butter, vanilla, cinnamon and nutmeg. Mix well.
Pour mixture into baking dish, place coconut on top of potato mixture and top with marshmallows. Bake for 10 to 15 minutes.
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