  We introduce and study a Serre functor in the category ${\cal P}_d$ of strict
polynomial functors over a field of positive characteristic. By using it we
obtain the Poincar\'e duality formula for Ext--groups from [C3] in elementary
way. We also show that the derived category of the category of affine strct
polynomial functors in some cases carries the structure of Calabi-Yau category.
