As is well known, the linear Sturm-Liouville eigenvalue problem on a bounded real interval [a, b] possesses a family of eigenfunctions which is a complete orthonormal system for the real Hilbert space L2[a, b], i.e. there exists a sequence of eigenfunctions un such that (ui, uj) = δij (Kronecker delta) for i, j ∈ N (the set of positive integers) and, if u ∈ L2[a, b], u = where cj = (u, uj). Pimbley (4, p. 113), raises the question as to whether similar completeness results hold for nonlinear problems. In this note we show that certain nonlinear Sturm-Liouville eigenvalue problems possess eigenfunctions which form a basis for L2[a, b], i.e. there exists a sequence of eigenfunctions {vn} for the nonlinear problem such that every u ∈ L2[a, b] can be expressed in the form u = by means of a unique sequence {cn} of real numbers.