Preheat oven to 350 degrees F (175 degrees C). Grease muffin cups or line with paper liners.
In a medium bowl, combine the flour, baking soda, baking powder, salt, cinnamon and nutmeg. In a large bowl, beat together the eggs, sugar, oil and vanilla until light and fluffy.
Stir in the zucchini until just blended. Add the flour mixture to the egg mixture and stir until just blended.
Fill each muffin cup about 2/3 full. Bake for 25 minutes in preheated oven or until a toothpick inserted into center of muffin comes out clean.