We apply first-principles calculations to predict the stability of porous nanotubes and fullerenes based on covalent organic frameworks (COF's). Two-dimensional COF's are extended sheets of covalently linked organic units forming porous materials composed only of light elements. We show that such sheets may be rolled up to form stable nanotubes, and, based on energetic aspects, even a fullerene-based COF might be observed. The electronic and elastic properties of COF nanotubes are also discussed. These materials might have interesting applications as molecular filters or carriers, in gas storage, or as building blocks for three-dimensional structures. (c) 2007 Elsevier B.V. All rights reserved.