Preheat the oven to 350°F. Lightly butter a cookie sheet. Combine the almonds, flour, baking soda, baking powder and salt in a medium mixing bowl.
In a separate bowl, cream the butter and sugar. Add eggs, one at a time. Add the lemon and orange zest and the vanilla extract. Add the almond mixture to the butter mixture and mix well to combine. (It will feel very sticky). Form the dough into two logs, approximately 8 inches long. Place on the cookie sheet, with at least two inches between them, and bake until they are just beginning to brown, about 20-25 minutes. When the logs are cool enough to handle, thinly slice on the diagonal. Return the biscotti to the oven and bake until crisp and golden brown, about 5 minutes on each side. Store in an airtight container.