  We consider linear spectral-meromorphic (s-meromorphic) OD operators at the
real axis such that all local solutions to the eigenvalue problems are
meromorphic for all $\lambda$. By definition, rank one algebro-geometrical
operator $L$ admit an OD operator $A$ such that $[L,A]=0$ and rank of this
commuting pair is equal to one. All of them are s-meromorphic. In particular,
second order ``singular soliton'' operators satisfy to this condition. Operator
$L^+$ formally adjoint to s-meromorphic operator $L$ is also s-meromorphic. For
singular eigenfunctions of operators $L,L^+$ following scalar product
$<f,g>=\int_R f\bar{g}dx$ is well-defined such that $<Lf,g>=<f,L^+g>$ avoiding
isolated singular points. For the case $L=L^+$ this formula defines indefinite
inner product on the spaces of singular functions $f,g\in F_L$ associated with
operator $L$. They are $C^{\infty}$ outside of singularities and have isolated
singularities of the same type as eigenfunctions $Lf=\lambda f$. Every
s-meromorphic operator can be approximated by algebro-geometric rank one
operators in any finite interval
