  Let F be a homotopy functor with values in the category of spectra. We show
that partially stabilized cross-effects of F have an action of a certain
operad. For functors from based spaces to spectra, it is the Koszul dual of the
little discs operad. For functors from spectra to spectra it is a desuspension
of the commutative operad. It follows that the Goodwillie derivatives of F are
a right module over a certain `pro-operad'. For functors from spaces to
spectra, the pro-operad is a resolution of the topological Lie operad. For
functors from spectra to spectra, it is a resolution of the trivial operad. We
show that the Taylor tower of the functor F can be reconstructed from this
structure on the derivatives.
