This paper considers the existence of Jost solutions f(k,r) and the Jost functions L(k) in the presence of redundant states. The definition of L(k) directly in terms of Fredholm determinants associated with kernels of integral equations is discussed. Examples are used to stress the importance of this relationship when the Jost solutions do not exist. NUCLEAR REACTIONS Antisymmetrization, redundant states, nonlocal potentials, Jost solutions and Jost functions. © 1979 The American Physical Society.