  In this paper we define 2-vector bundles as suitable bundles of 2-vector
spaces over a base space, and compare the resulting 2-K-theory with the
algebraic K-theory spectrum K(V) of the 2-category of 2-vector spaces, as well
as the algebraic K-theory spectrum K(ku) of the connective topological K-theory
spectrum ku. We explain how K(ku) detects v_2-periodic phenomena in stable
homotopy theory, and as such is a form of elliptic cohomology.
