  We obtain a description of the Fu\v{c}ik spectrum associated to the
one-dimensional asymmetric problem with indefinite weights $Lu = am(t)u^+ -
bn(t)u^-$ in $]T_1, T_2[$, $u'(T_1) = 0 = u'(T_2)$, where $L$ is a
Sturm-Liouville operator. Our approach is based on the shooting method.
