This paper concerns with the nodal properties of the eigenfunctions (Fučik eigenfunctions) of , where , is the -Laplacian. More precisely, the authors study the properties of the nonlinear eigenvalue problem
and its more general version
where is a bounded domain in with smooth boundary , and are real spectral parameters. The authors prove that, if is an eigenfunction associated with the th variational eigenvalue, , then has at most nodal domains. Moreover, if has nodal domains then there is another eigenfunction with at most nodal domains.