Combine the egg whites with the sugar in a saucepan and mix well.
Place over medium heat and stir in the coconut, mixing well.
Cook over low heat, stirring continuously, for about 10 minutes, or until the mixture thickens.
Remove from heat and set aside to cool.
Oil or spray Pam on a baking sheet and drop the mixture by rounded spoonfuls onto the sheet, spacing the cookies about 1-inch apart.
Bake at 300 degrees for 15 to 20 minutes or until they are a light golden brown.
Transfer to wire racks to cool.
These cookies keep well in covered cookie jars.