Combine sugar, brown sugar, flour, cornstarch, cinnamon and nutmeg in a large bowl. Stir in rhubarb and strawberries. Mix well and spoon mixture into pastry lined pie plate. Lay top layer of pastry over the pie and seal the edges.
Bake for 10 minutes. Reduce heat to 350ºF and bake for 45 to 50 minutes more until pastry is golden and the filling is bubbling.