  We explain how nonperturbative effects can be systematically included when
constructing an effective field theory. We concentrate in particular on the
matching calculation, by which a low energy theory without a heavy particle
degree of freedom is matched onto the full theory. The matching calculation
requires some new formalism, because for a large class of theories, instantons
occur in a continuous range of scales from far below the mass of the heavy
particle to far above. We show how the complete IR finiteness of the usual
matching formalism arises in this new context. As an example, we formally
integrate out a heavy quark in QCD. %%%% Includes 14 PiCTeX figures. %%%%
