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We study the superconducting instability in systems with long but finiteranged, attractive, pairing interactions. We show that such long-rangedsuperconductors exhibit a new class of fluctuations in which the internalstructure of the Cooper pair wave function is soft, and thus lead to"pseudogap" behavior in which the actual transition temperature is greatlydepressed from its mean field value. These fluctuations are {\it not} phasefluctuations of the standard superconducting order parameter, and lead to ahighly unusual Ginzburg-Landau description. We suggest that the crossoverbetween the BCS limit of a short-ranged attraction and our problem is ofinterest in the context of superconductivity in the underdoped cuprates.Comment: 20 pages with one embedded ps figure. Minor revisions to the text and  references. Final version to appear in PRB on Nov. 1st, 200

Low-energy collective modes, Ginzburg-Landau theory, and pseudogap behavior in superconductors with long-range pairing interactions