Preheat oven to 180 C / Gas 4. Lightly grease and flour a 23cm square cake tin.
Sir together flour, baking powder, salt, cinnamon and nutmeg.
In a large bowl, cream margarine and brown sugar, beating until light and fluffy. Beat in eggs and vanilla. Stir flour mixture into creamed mixture alternately with apple sauce; make 3 dry and 2 liquid additions, combining lightly after each. Spoon cake mixture into the cake tin.
Bake for 40 to 45 minutes, or until cake springs back when lightly touched.