In a large bowl, combine the flour, sugar, baking soda, allspice, baking powder and salt. In another bowl, beat the eggs, oil and vanilla; add squash and bananas. Stir into dry ingredients just until moistened. Fold in walnuts.
Pour into two greased 8-in. x 4-in. loaf pans. Bake at 350° for 55-60 minutes or until a toothpick inserted near the center comes out clean. Cool for 10 minutes before removing from pans to wire racks.
You might need to use more time when baking 2 loaves.